bluuebunny/crossref_metadata_2025 huggingface dataset:
A systematic review on hydroxyurea therapy for sickle cell disease in India
Authors: Pandey Apoorva , Kaur Harpreet , Borah Sapan , Khargekar Naveen , Karra Vijay Kumar , Adhikari Tulsi , Jain Dipty , Madkaikar Manisha
Published: January 2023

Background & objectives:

Sickle cell disease (SCD) constitutes frequently inherited haemoglobin disorders and poses a significant health burden in India. Hydroxyurea (HU), the most commonly used drug, has shown promising results in the clinical management of SCD. The present systematic review was undertaken to assess the efficacy and toxicity of HU in Indian sickle cell patients.

Methods:

A systematic review of studies on HU therapy was conducted to identify the application of HU and its outcome(s) across India. PubMed, Scopus and Cochrane Library was used as data sources for various studies on the efficacy and toxicity of HU therapy for treatment for SCD in India published between January 2001 and October 2021. Two authors independently extracted the data on study design, patient characteristics and therapeutic outcomes of HU in order to determine the study quality of the present review.

Results:

Overall, 14 studies were included for a systematic analysis. Of these 11 were prospective, two cross-sectional and one double-blind randomized controlled trial. Low-dose HU (10 mg/kg/day) was found to reduce the rates of vaso-occlusive crisis and hospitalization as well as decreased the requirement of blood transfusion in SCD patients. The foetal haemoglobin (HbF) level was recorded in 13 (80%) studies all of whom reported an elevation in the HbF levels, with a mean increase in per cent HbF from 15.8 to 21.4 per cent across studies. The common adverse events were reversible, mild-to-moderate cytopenia and anaemia.

Interpretation & conclusions:

The findings of the present review suggest that there is still insufficient information presently to determine the long-term or major adverse effects on organ damage, fertility as well as pregnancy on the use of HU therapy for SCD. Long-term multi-centric studies are thus required to address these problems.
Identification of Genes Involved in EGF-induced Apoptosis Using CRISPR/Cas9 Knockout Screening: Implications for Novel Therapeutic Targets in EGFR-Overexpressing Cancers
Authors: Kim Jae Sik , Lee Joo Ho , Jeon Sang-Rok , Kim Yongsub , Jeon Seung Hyuck , Wu Hong-Gyun
Published: January 2023

Purpose Exogenous epidermal growth factor (EGF) causes apoptosis in EGF receptor (EGFR)–overexpressing cell lines. The apoptosis-inducing factors could be a therapeutic target. We aimed to determine the mechanism of EGF-induced apoptosis using a genome-wide clustered regularly interspaced short palindromic repeats (CRISPR)-based knockout screen.Materials and Methods Two-vector system of the human genome-scale CRISPR knockout library v2 was used to target 19,050 genes using 123,411 single guide RNAs (sgRNAs). Recombinant human EGF (100 nM) or distilled water four times was administered to the experimental and control groups, respectively. The read counts of each sgRNA obtained from next-generation sequencing were analyzed using the edgeR algorithm. We used another EGFR-overexpressing cell line (A549) and short hairpin RNAs (shRNAs) targeting five EGF-resistance genes for validation. DUSP1 expression in A431, A549, and HEK293FT cells was calculated using reverse transcription–quantitative polymerase chain reaction.Results We found 77 enriched and 189 depleted genes in the experimental group using the CRISPR-based knockout screen and identified the top five EGF-resistance genes: DDX20, LHFP, REPS1, DUSP1,<.i> and KRTAP10-12. Transfecting shRNAs targeting these genes into A549 cells significantly increased the surviving fractions after EGF treatment, compared with those observed in the control shRNA-transfected cells. The expression ratio of DUSP1 (inhibits ERK signaling) increased in A431 and A549 cells after EGF treatment. However, DUSP1 expression remained unchanged in HEK293FT cells after EGF treatment.Conclusion The CRISPR-based knockout screen revealed 266 genes possibly responsible for EGF-induced apoptosis. DUSP1 might be a critical component of EGF-induced apoptosis and a novel target for EGFR-overexpressing cancers.
Rolling factors deformations and extensions of canonical curves
Authors: Stevens Jan
Published: January 2023

A tetragonal canonical curve is the complete intersection of two divisors on a scroll. The equations can be written in 'rolling factors' format. For such homogeneous ideals we give methods to compute infinitesimal deformations. Deformations can be obstructed. For the case of quadratic equations on the scroll we derive explicit base equations. They are used to study extensions of tetragonal curves.
On the derived category of sheaves on a manifold
Authors: Neeman Amnon
Published: January 2023

Let

M

be a non-compact, connected manifold of dimension

\geq 1

. Let

D(\text{sheaves}/M)

be the unbounded derived category of chain complexes of sheaves of abelian groups on

M

. We prove that

D(\text{sheaves}/M)

is not a compactly generated triangulated category, but is well generated.
Effective freeness of adjoint line bundles
Authors: Heier Gordon
Published: January 2023

This note shows how two existing approaches to providing effective (quadratic) bounds for the freeness of adjoint line bundles can be linked to establish a new effective bound which approximately differs from the linear bound conjectured by Fujita only by a factor of the cube root of the dimension of the underlying manifold. As an application, a new effective statement for pluricanonical embeddings is derived.
Complex structure on the smooth dual of $GL(n)$
Authors: Brodzki Jacek , Plymen Roger
Published: January 2023

Let

G

denote the

p

-adic group

GL(n)

, let

\Pi(G)

denote the smooth dual of

G

, let

\Pi(\Omega)

denote a Bernstein component of

\Pi(G)

and let

\mathcal H(\Omega)

denote a Bernstein ideal in the Hecke algebra

\mathcal H(G)

. With the aid of Langlands parameters, we equip

\Pi(\Omega)

with the structure of complex algebraic variety, and prove that the periodic cyclic homology of

\mathcal{H}(\Omega)

is isomorphic to the de Rham cohomology of

\Pi(\Omega)

. We show how the structure of the variety

\Pi(\Omega)

is related to Xi's affirmation of a conjecture of Lusztig for

GL(n, \mathbb{C})

. The smooth dual

\Pi(G)

admits a deformation retraction onto the tempered dual

\Pi^t(G)

.
Rost projectors and Steenrod operations
Authors: Karpenko Nikita , Merkurjev Alexander
Published: January 2023

Let

X

be an anisotropic projective quadric possessing a Rost projector

\rho

. We compute the 0-dimensional component of the total Steenrod operation on the modulo 2 Chow group of the Rost motive given by the projector

\rho

. The computation allows to determine the whole Chow group of the Rost motive and the Chow group of every excellent quadric (the results announced by Rost). On the other hand, the computation is being applied to give a simpler proof of Vishik's theorem stating that the integer

\dim X+1

is a power of 2.
Toric hyperkähler varieties
Authors: Hausel Tamás , Sturmfels Bernd
Published: January 2023

Extending work of Bielawski-Dancer citeBD and Konno citeKo, we develop a theory of toric hyperkähler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawrence toric varieties, meaning GIT quotients of even-dimensional affine spaces by symplectic torus actions. A toric hyperkähler variety is a complete intersection in a Lawrence toric variety. Both varieties are non-compact, and they share the same cohomology ring, namely, the Stanley-Reisner ring of a matroid modulo a linear system of parameters. Familiar applications of toric geometry to combinatorics, including the Hard Lefschetz Theorem and the volume polynomials of Khovanskii-Pukhlikov citeKP, are extended to the hyperkähler setting. When the matroid is graphic, our construction gives the toric quiver varieties, in the sense of Nakajima citeNa.
Reconstruction phases for Hamiltonian systems on cotangent bundles
Authors: Blaom Anthony D.
Published: January 2023

Reconstruction phases describe the motions experienced by dynamical systems whose symmetry-reduced variables are undergoing periodic motion. A well known example is the non-trivial rotation experienced by a free rigid body after one period of oscillation of the body angular momentum vector. Here reconstruction phases are derived for a general class of Hamiltonians on a cotangent bundle

{\mathrm T}^*Q

possessing a group of symmetries

G

, and in particular for mechanical systems. These results are presented as a synthesis of the known special cases

Q=G

and

G

Abelian, which are reviewed in detail.
A short proof of Rost nilpotence via refined correspondences
Authors: Brosnan Patrick
Published: January 2023

I generalize the notion of composition of algebraic correspondences using the refined Gysin homorphism of Fulton–MacPherson intersection theory. Using this notion, I give a short self-contained proof of Rost's “nilpotence theorem” and a generalization of one important proposition used by Rost in his proof of the theorem.
Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others
Authors: Filonov N. , Klopp F.
Published: January 2023

We prove that the spectrum of a Schrödinger operator with a potential which is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous. Therefore, we reduce the operator using the Bloch-Floquet-Gelfand transform in the periodic variables, and show that, except for at most a set of quasi-momenta of measure zero, the reduced operators satisfies a limiting absorption principle.
Nodal domain theorems à la Courant
Authors: Ancona A. , Helffer B. , Hoffmann-Ostenhof T.
Published: January 2023

Let

H(\Omega_0)=-\Delta+V

be a Schrödinger operator on a bounded domain

\Omega_0\subset \mathbb R^d (d\geq 2)

with Dirichlet boundary condition. Suppose that

\Omega_\ell (\ell \in \{1,\dots,k\})

are some pairwise disjoint subsets of

\Omega_0

and that

H(\Omega_\ell)

are the corresponding Schrödinger operators again with Dirichlet boundary condition. We investigate the relations between the spectrum of

H(\Omega_0)

and the spectra of the

H(\Omega_\ell)

. In particular, we derive some inequalities for the associated spectral counting functions which can be interpreted as generalizations of Courant's nodal theorem. For the case where equality is achieved we prove converse results. In particular, we use potential theoretic methods to relate the

\Omega_\ell

to the nodal domains of some eigenfunction of

H(\Omega_0)

.
Tight embeddings of simply connected $4$-manifolds
Authors: Kühnel Wolfgang
Published: January 2023

The classification of compact and simply connected PL 4-manifolds states that the homeomorphism classes coincide with the homotopy classes, and that these are classified by the intersection form. We show here that “most” of these classes with an indefinite intersection form can be represented by a tight polyhedral embedding into some Euclidean space. It remains open which of the PL structures can be realized in such a way.
Projective bundle theorem in homology theories with Chern structure
Authors: Nenashev Alexander
Published: January 2023

Panin and Smirnov deduced the existence of push-forwards, along projective morphisms, in a cohomology theory with cup products, from the assumption that the theory is endowed with an extra structure called orientation. A part of their work is a proof of the Projective Bundle Theorem in cohomology based on the assumption that we have the first Chern class for line bundles. In some examples we have to consider a pair of theories, cohomology and homology, related by a cap product. It would be useful to construct transfer maps (pull-backs) along projective morphisms in homology in such a situation under similar assumptions. In this note we perform the projective bundle theorem part of this project in homology.
Vanishing theorems and degeneracy loci in small corang
Authors: Chaput Pierre-Emmanuel
Published: January 2023

After giving an explicit description of all the non vanishing Dolbeault cohomology groups of ample line bundles on grassmannians, I give two series of vanishing theorems for ample vector bundles on a smooth projective variety. They imply a part of a conjecture by Fulton and Lazarsfeld about the connectivity of some degeneracy loci.
On the Chow groups of quadratic Grassmannians
Authors: Vishik A.
Published: January 2023

In this text we get a description of the Chow-ring (modulo 2) of the Grassmanian of the middle-dimensional planes on arbitrary projective quadric. This is only a first step in the computation of the, so-called, generic discrete invariant of quadrics. This generic invariant contains the “splitting pattern” and “motivic decomposition type” invariants as specializations. Our computation gives an important invariant

J(Q)

of the quadric

Q

. We formulate a conjecture describing the canonical dimension of

Q

in terms of

J(Q)

.
On the torsion of the Mordell-Weil group of the Jacobian of Drinfeld modular curves
Authors: Pál Ambrus
Published: January 2023

Let

Y_0(\mathfrak p)

be the Drinfeld modular curve parameterizing Drinfeld modules of rank two over

\Bbb F_q[T]

of general characteristic with Hecke level

\mathfrak p

-structure, where

\mathfrak p\triangleleft\Bbb F_q[T]

is a prime ideal of degree

d

. Let

J_0(\mathfrak p)

denote the Jacobian of the unique smooth irreducible projective curve containing

Y_0(\mathfrak p)

. Define

N(\mathfrak p)=\frac{q^d-1}{q-1}

, if

d

is odd, and define

N(\mathfrak p)=\frac{q^d-1}{q^2-1}

, otherwise. We prove that the torsion subgroup of the group of

\Bbb F_q(T)

-valued points of the abelian variety

J_0(\mathfrak p)

is the cuspidal divisor group and has order

N(\mathfrak p)

. Similarly the maximal

\mu

-type finite étale subgroup-scheme of the abelian variety

J_0(\mathfrak p)

is the Shimura group scheme and has order

N(\mathfrak p)

. We reach our results through a study of the Eisenstein ideal

\mathfrak E(\mathfrak p)

of the Hecke algebra

\Bbb T(\mathfrak p)

of the curve

Y_0(\mathfrak p)

. Along the way we prove that the completion of the Hecke algebra

\Bbb T(\mathfrak p)

at any maximal ideal in the support of

\mathfrak E(\mathfrak p)

is Gorenstein.
Moduli schemes of generically simple Azumaya modules
Authors: Hoffmann Norbert , Stuhler Ulrich
Published: January 2023

Let A be an Azumaya algebra over a smooth projective variety X or more generally, a torsion free coherent sheaf of algebras over X whose generic fiber is a central simple algebra. We show that generically simple torsion free A-module sheaves have a projective coarse moduli scheme; it is smooth and even symplectic if X is an abelian or K3 surface and A is Azumaya. We explain a relation to the classical theory of the Brandt groupoid.
Slope filtrations revisited
Authors: Kedlaya Kiran S.
Published: January 2023

We give a “second generation” exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism of stable vector bundles.
Bifurcation from relative equilibria of noncompact group actions: Skew products, meanders, and drifts
Authors: Fiedler Bernold , Sandstede Björn , Scheel Arnd , Wulff Claudia
Published: January 2023

We consider a finite-dimensional, typically noncompact Riemannian manifold

M

with a differentiable proper action of a possibly non-compact Lie group

G.

We describe

G

-equivariant flows in a tubular neighborhood

U

of a relative equilibrium

G\cdot u_0,u_0\in M

, with compact isotropy

H

of

u_0,

by a skew product flow

\dot{g} = g {\bf a}(v),\dot{v} = \varphi(v).

Here

g\in G, {\bf a}\in {\rm alg}(G).

The vector

v

is in a linear slice

V

to the group action. The induced local flow on

G\times V

is equivariant under the action of

(g_0,h)\in G\times H

on

(g,v)\in G\times V,

given by

(g_0,h)(g,v) = (g_0 gh^{-1},hv).

The original flow on

U

is equivalent to the induced flow on

\{id\}\times H

-orbits in

G\times V.

Applications to relative equivariant Hopf bifurcation in V are presented, clarifying phenomena like periodicity, meandering, and drifting. Specific illustrations involving Euclidean groups

G

are meandering spirals, in the plane, and drifting twisted scroll rings, in three-dimensional Belousov-Zhabotinsky media.
Sobolev spaces on Lie manifolds and regularity for polyhedral domains
Authors: Ammann Bernd , Ionescu Alexandru D. , Nistor Victor
Published: January 2023

We study some basic analytic questions related to differential operators on Lie manifolds, which are manifolds whose large scale geometry can be described by a a Lie algebra of vector fields on a compactification. We extend to Lie manifolds several classical results on Sobolev spaces, elliptic regularity, and mapping properties of pseudodifferential operators. A tubular neighborhood theorem for Lie submanifolds allows us also to extend to regular open subsets of Lie manifolds the classical results on traces of functions in suitable Sobolev spaces. Our main application is a regularity result on polyhedral domains

\mathbb P \subset \mathbb R^3

using the weighted Sobolev spaces

\mathcal K^m_a(\mathbb P)

. In particular, we show that there is no loss of

\mathcal K^m_a

–regularity for solutions of strongly elliptic systems with smooth coefficients. For the proof, we identify

\mathcal K^m_a(\mathbb P)

with the Sobolev spaces on

\mathbb P

associated to the metric

r_{\mathbb P}^{-2} g_E

, where

g_E

is the Euclidean metric and

r_{\mathbb P}(x)

is a smoothing of the Euclidean distance from

x

to the set of singular points of

\mathbb P

. A suitable compactification of the interior of

\mathbb P

then becomes a regular open subset of a Lie manifold. We also obtain the well-posedness of a non-standard boundary value problem on a smooth, bounded domain with boundary

\mathcal O \subset \mathbb R^n

using weighted Sobolev spaces, where the weight is the distance to the boundary.
A symplectic approach to van den Ban's convexity theorem
Authors: Otto Michael , Foth Philip
Published: January 2023

Let

G

be a complex semisimple Lie group and

\tau

a complex antilinear involution that commutes with a Cartan involution. If

H

denotes the connected subgroup of

\tau

-fixed points in

G

, and

K

is maximally compact, each

H

-orbit in

G/K

can be equipped with a Poisson structure as described by Evens and Lu. We consider symplectic leaves of certain such

H

-orbits with a natural Hamiltonian torus action. A symplectic convexity theorem then leads to van den Ban's convexity result for (complex) semisimple symmetric spaces.
Volumes of symmetric spaces via lattice points
Authors: Gillet Henri , Grayson Daniel R.
Published: January 2023

We show how to use elementary methods to compute the volume of

Sl_k R/Sl_k Z

. We compute the volumes of certain unbounded regions in Euclidean space by counting lattice points and then appeal to the machinery of Dirichlet series to get estimates of the growth rate of the number of lattice points appearing in the region as the lattice spacing decreases. We also present a proof of the closely related result that the Tamagawa number is 1.
Equivariant Iwasawa theory: an example
Authors: Ritter Jürgen , Weiss Alfred
Published: January 2023

The equivariant main conjecture of Iwasawa theory is shown to hold for a Galois extension

K/k

of totally real number fields with Galois group an

l

-adic pro-

l

Lie group of dimension 1 containing an abelian subgroup of index

l

, provided that Iwasawa's

\mu

-invariant

\mu(K/k)

vanishes.
$C^*$-algebras associated to coverings of $k$-graphs
Authors: Kumjian Alex , Pask David , Sims Aidan
Published: January 2023

A covering of

k

-graphs (in the sense of Pask–Quigg–Raeburn) induces an embedding of universal

C^*

-algebras. We show how to build a

(k+1)

-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct limit of

k

-graph algebras under embeddings induced from coverings as the universal algebra of a

(k+1)

-graph. Our main focus is on computing the

K

-theory of the

(k+1)

-graph algebra from that of the component

k

-graph algebras. Examples of our construction include a realisation of the Kirchberg algebra

\mathcal{P}_n

whose

K

-theory is opposite to that of

\mathcal{O}_n

, and a class of A

\mathbf T

-algebras that can naturally be regarded as higher-rank Bunce–Deddens algebras.
Schur class operator functions and automorphisms of Hardy algebras
Authors: Muhly Paul S. , Solel Baruch
Published: January 2023

Let

E

be a

W^{\ast}

-correspondence over a von Neumann algebra

M

and let

H^{\infty}(E)

be the associated Hardy algebra. If

\sigma

is a faithful normal representation of

M

on a Hilbert space

H

, then one may form the dual correspondence

E^{\sigma}

and represent elements in

H^{\infty}(E)

as

B(H)

-valued functions on the unit ball

\mathbb{D}(E^{\sigma})^{\ast}

. The functions that one obtains are called Schur class functions and may be characterized in terms of certain Pick-like kernels. We study these functions and relate them to system matrices and transfer functions from systems theory. We use the information gained to describe the automorphism group of

H^{\infty}(E)

in terms of special Möbius transformations on

\mathbb{D}(E^{\sigma})

. Particular attention is devoted to the

H^{\infty}

-algebras that are associated to graphs.
Brascamp--Lieb inequalities for non-commutative integration
Authors: Carlen Eric A. , Lieb Elliott H.
Published: January 2023

We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings.
Natural $G$-constellation families
Authors: Logvinenko Timothy
Published: January 2023

Let

G

be a finite subgroup of

\operatorname{GL}_n(\mathbb{C}). G

-constellations are a scheme-theoretic generalization of orbits of

G

in

\mathbb{C}^n

. We study flat families of

G

-constellations parametrised by an arbitrary resolution of the quotient space

\mathbb{C}^n/G

. We develop a geometrical naturality criterion for such families, and show that, for an abelian

G

, the number of equivalence classes of these natural families is finite. The main intended application is the derived McKay correspondence.
On the motivic spectra representing algebraic cobordism and algebraic $K$-theory
Authors: Gepner David , Snaith Victor
Published: January 2023

We show that the motivic spectrum representing algebraic

K

-theory is a localization of the suspension spectrum of

\mathbb{P}^\infty

, and similarly that the motivic spectrum representing periodic algebraic cobordism is a localization of the suspension spectrum of

BGL

. In particular, working over

\mathbb{C}

and passing to spaces of

\mathbb{C}

-valued points, we obtain new proofs of the topological versions of these theorems, originally due to the second author. We conclude with a couple of applications: first, we give a short proof of the motivic Conner-Floyd theorem, and second, we show that algebraic

K

-theory and periodic algebraic cobordism are

E_\infty

motivic spectra.
$p$-adic monodromy of the universal deformation of a HW-cyclic Barsotti–Tate group
Authors: Tian Yichao
Published: January 2023

Let

k

be an algebraically closed field of characteristic

p>0

, and

G

be a Barsotti–Tate over

k

. We denote by

\mathbf S

the “algebraic” local moduli in characteristic

p

of

G

, by

\mathbf G

the universal deformation of

G

over

\mathbf S

, and by

\mathbf U\subset\mathbf S

the ordinary locus of

\mathbf G

. The étale part of

\mathbf G

over

\mathbf U

gives rise to a monodromy representation

\rho_{\mathbf G}

of the fundamental group of

\mathbf U

on the Tate module of

\mathbf G

. Motivated by a famous theorem of Igusa, we prove in this article that

\rho_{\mathbf G}

is surjective if

G

is connected and HW-cyclic. This latter condition is equivalent to saying that Oort's

a

-number of

G

equals 1, and it is satisfied by all connected one-dimensional Barsotti–Tate groups over

k

.
Hyperbolic geometry on noncommutative balls
Authors: Popescu Gelu
Published: January 2023

In this paper, we study the noncommutative balls

\mathcal C_\rho:={(X_1,\ldots, X_n)\in B(\mathcal H)^n: \ \omega_\rho(X_1,\ldots, X_n)\leq 1},\qquad \rho\in (0,\infty],

where

\omega_\rho

is the joint operator radius for

n

-tuples of bounded linear operators on a Hilbert space. In particular,

\omega_1

is the operator norm,

\omega_2

is the joint numerical radius, and

\omega_\infty

is the joint spectral radius. We introduce a Harnack type equivalence relation on

\mathcal C_\rho, \rho>0

, and use it to define a hyperbolic distance

\delta_\rho

on the Harnack parts (equivalence classes) of

\mathcal C_\rho

. We prove that the open ball

[\mathcal C_\rho]_{<1}:={(X_1,\ldots, X_n)\in B(\mathcal H)^n: \ \omega_\rho(X_1,\ldots, X_n)<1},\qquad \rho>0,

is the Harnack part containing 0 and obtain a concrete formula for the hyperbolic distance, in terms of the reconstruction operator associated with the right creation operators on the full Fock space with

n

generators. Moreover, we show that the

\delta_\rho

-topology and the usual operator norm topology coincide on

[\mathcal C_\rho]_{<1}

. While the open ball

[\mathcal C_\rho]_{<1}

is not a complete metric space with respect to the operator norm topology, we prove that it is a complete metric space with respect to the hyperbolic metric

\delta_\rho

. In the particular case when

\rho=1

and

\mathcal H=\mathbb C

, the hyperbolic metric

\delta_\rho

coincides with the Poincaré–Bergman distance on the open unit ball of

\mathbb C^n

. We introduce a Carathéodory type metric on

[\mathcal C_\infty]_{<1}

, the set of all

n

-tuples of operators with joint spectral radius strictly less then 1, by setting

d_K(A,B)=\sup_p \|\mathfrak R p(A)-\mathfrak R p(B)\|,\qquad A,B\in [\mathcal C_\infty]_{<1},

where the supremum is taken over all noncommutative polynomials with matrix-valued coefficients

p\in \mathbb C[X_1,\ldots, X_n]\otimes M_{m}, m\in \mathbb N

, with

\mathfrak R p(0)=I

and

\mathfrak R p(X)\geq 0

for all

X\in \mathcal C_1

. We obtain a concrete formula for

d_K

in terms of the free pluriharmonic kernel on the noncommutative ball

[\mathcal C_\infty]_{<1}

. We also prove that the metric

d_K

is complete on

[\mathcal C_\infty]_{<1}

and its topology coincides with the operator norm topology. We provide mapping theorems, von Neumann inequalities, and Schwarz type lemmas for free holomorphic functions on noncommutative balls, with respect to the hyperbolic metric

\delta_\rho

, the Carathéodory metric

d_K

, and the joint operator radius

\omega_\rho, \rho\in (0,\infty]

.
On proper $\mathbb R$-actions on hyperbolic Stein surfaces
Authors: Miebach Christian , Oeljeklaus Karl
Published: January 2023

In this paper we investigate proper

\mathbb{R}

-actions on hyperbolic Stein surfaces and prove in particular the following result: Let

D\subset\mathbb{C}^2

be a simply-connected bounded domain of holomorphy which admits a proper

\mathbb{R}

-action by holomorphic transformations. The quotient

D/\mathbb Z

with respect to the induced proper

\mathbb{Z}

-action is a Stein manifold. A normal form for the domain

D

is deduced.
Invariant inner product in spaces of holomorphic functions on bounded symmetric domains
Authors: Arazy Jonathan , Upmeier Harald
Published: January 2023

We provide new integral formulas for the invariant inner product on spaces of holomorphic functions on bounded symmetric domains of tube type.
$\Bbb Q$-Fano threefolds of large Fano index. I.
Authors: Prokhorov Yuri
Published: January 2023

We study Q-Fano threefolds of large Fano index. In particular, we prove that the maximum possible Fano index is attained only by the weighted projective space

P(3,4,5,7)

.
Remarks on the Darboux transform of isothermic surfaces
Authors: Hertrich-Jeromin Udo , Pedit Franz
Published: January 2023

We study Darboux and Christoffel transforms of isothermic surfaces in Euclidean space. Using quaternionic calculus we derive a Riccati type equation which characterizes all Darboux transforms of a given isothermic surface. Surfaces of constant mean curvature turn out to be special among all isothermic surfaces: their parallel surfaces of constant mean curvature are Christoffel and Darboux transforms at the same time. We prove – as a generalization of Bianchi's theorem on minimal Darboux transforms of minimal surfaces – that constant mean curvature surfaces in Euclidean space allow

\infty^3

Darboux transforms into surfaces of constant mean curvature. We indicate the relation between these Darboux transforms and Bäcklund transforms of spherical surfaces.
Dimensions of affine Deligne-Lusztig varieties in affine flag varieties.
Authors: Görtz Ulrich , He Xuhua
Published: January 2023

Affine Deligne-Lusztig varieties are analogs of Deligne-Lusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper [5] by Haines, Kottwitz, Reuman, and the first named author, about the question which affine Deligne-Lusztig varieties (for a split group and a basic

\sigma

-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a classical group and the chosen basic

\sigma

-conjugacy class is the class of

b=1

, we also prove the dimension formula predicted in op. cit. in almost all cases.
Bundles, cohomology and truncated symmetric polynomials
Authors: Adem Alejandro , Reichstein Zinovy
Published: January 2023

The cohomology of the classifying space

BU(n)

of the unitary group can be identified with the the ring of symmetric polynomials on

n

variables by restricting to the cohomology of

BT

, where

T\subset U(n)

is a maximal torus. In this paper we explore the situation where

BT = (\ CP^{\infty})^n

is replaced by a product of finite dimensional projective spaces

(\ CP^d)^n

, fitting into an associated bundle

U(n)\times_T (\ S^{2d+1})^n\to (\ CP^d)^n\to BU(n).

We establish a purely algebraic version of this problem by exhibiting an explicit system of generators for the ideal of truncated symmetric polynomials. We use this algebraic result to give a precise descriptions of the kernel of the homomorphism in cohomology induced by the natural map

(\ CP^d)^n\to BU(n)

. We also calculate the cohomology of the homotopy fiber of the natural map

E S_n\times_{S_n}(\ CP^d)^n\to BU(n)

.
Dilation theory, commutant lifting and semicrossed products
Authors: Davidson K.R. , Katsoulis E.G.
Published: January 2023

We take a new look at dilation theory for nonself-adjoint operator algebras. Among the extremal (co)extensions of a representation, there is a special property of being fully extremal. This allows a refinement of some of the classical notions which are important when one moves away from standard examples. We show that many algebras including graph algebras and tensor algebras of C*-correspondences have the semi-Dirichlet property which collapses these notions and explains why they have a better dilation theory. This leads to variations of the notions of commutant lifting and Ando's theorem. This is applied to the study of semicrossed products by automorphisms, and endomorphisms which lift to the C*-envelope. In particular, we obtain several general theorems which allow one to conclude that semicrossed products of an operator algebra naturally imbed completely isometrically into the semicrossed product of its C*-envelope, and the C*-envelopes of these two algebras are the same.
Green functions via hyperbolic localization
Authors: Achar Pramod N.
Published: January 2023

Let

G

be a reductive algebraic group, with nilpotent cone

\mathcal N

and flag variety

\mathcal B

. We construct an exact functor from perverse sheaves on

\mathcal N

to locally constant sheaves on

\mathcal B

, and we use it to study Ext-groups and stalks of simple perverse sheaves on

\mathcal N

in terms of the cohomology of

\mathcal B

.
Change of Selmer group for big Galois representations and application to normalization
Authors: Arnold Trevor , Koo Koopa Tak-Lun
Published: January 2023

The goal of this note is to prove, under some assumptions, a formula relating the Selmer groups of isogenous Galois representations. Local and global Euler-Poincaré characteristic formulas are key tools in the proof. With additional hypotheses, we use the isogeny formula to study how the formation of Selmer groups interacts with normalization of the coefficient ring and discuss how a main conjecture for a big Galois representation over a non-normal ring follows from a corresponding conjecture over the normalization.
The singularity category of an algebra with radical square zero
Authors: Chen Xiao-Wu
Published: January 2023

To an artin algebra with radical square zero, a regular algebra in the sense of von Neumann and a family of invertible bimodules over the regular algebra are associated. These data describe completely, as a triangulated category, the singularity category of the artin algebra. A criterion on the Hom-finiteness of the singularity category is given in terms of the valued quiver of the artin algebra.
Smooth representations of ${GL}_m(D)$. V: Endo-classes
Authors: Broussous P. , Sécherre V. , Stevens S.
Published: January 2023

Let

\mathrm F

be a locally compact nonarchimedean local field. In this article, we extend to any inner form of

\operatorname{GL}_n

over

\mathrm F

, with

n\geqslant 1

, the notion of endo-class introduced by Bush­nell and Henniart for

\operatorname{GL}_n(\mathrm F)

. We investigate the intertwining relations of simple characters of these groups, in particular their preservation properties under transfer. This allows us to associate to any discrete series representation of an inner form of

\operatorname{GL}_n(\mathrm F)

an endo-class over

\mathrm F

. We conjecture that this endo-class is invariant under the local Jacquet–Langlands correspondence.
Basic polynomial invariants, fundamental representations and the Chern class map
Authors: Baek Sanghoon , Neher Erhard , Zainoulline Kirill
Published: January 2023

Consider a crystallographic root system together with its Weyl group

W

acting on the weight lattice

\Lambda

. Let

\mathbb Z[\Lambda]^W

and

S(\Lambda)^W

be the

W

-invariant subrings of the integral group ring

\mathbb Z[\Lambda]

and the symmetric algebra

S(\Lambda)

respectively. A celebrated result by Chevalley says that

\mathbb Z[\Lambda]^W

is a polynomial ring in classes of fundamental representations

\rho_1,...,\rho_n

and

S(\Lambda)^W\otimes{Q}

is a polynomial ring in basic polynomial invariants

q_1,...,q_n

. In the present paper we establish and investigate the relationship between

\rho_i

's and

q_i

's over the integers. As an application we provide estimates for the torsion of the Grothendieck

\gamma

-filtration and the Chow groups of some twisted flag varieties up to codimension 4.
Fermion correlation inequalities derived from G- and P-conditions
Authors: Bach Volker , Knörr Hans Konrad , Menge Edmund
Published: January 2023

It is shown in this paper that the G-Condition and the P-Condition from representability imply the fermion correlation estimate from [1] which, in turn, is known to yield a nontrivial bound on the accuracy of the Hartree–Fock approximation for large Coulomb systems.
Moduli spaces of flat connections and Morita equivalence of quantum tori
Authors: Severa Pavol
Published: January 2023

We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras. The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure (such as symplectic groupoid structure) gets a geometrical explanation via 3-dimensional cobordisms. We give a formula for the symplectic form in terms of holonomies, based on a central extension of the gauge group by closed 2-forms. This construction is finally used for a certain extension of the Morita equivalence of quantum tori to the world of Poisson-Lie groups.
Remarks on filtrations of the homology of real varieties
Authors: Heller Jeremiah , Voineagu Mircea
Published: January 2023

We demonstrate that a conjecture of Teh which relates the niveau filtration on Borel-Moore homology of real varieties and the images of generalized cycle maps from reduced Lawson homology is false. We show that the niveau filtration on reduced Lawson homology is trivial and construct an explicit class of examples for which Teh's conjecture fails by generalizing a result of Schülting. We compare different cycle maps and in particular we show that the Borel-Haeflinger cycle map naturally factors through the reduced Lawson homology cycle map.
Hodge-Witt cohomology and Witt-rational singularities
Authors: Chatzistamatiou Andre , Rülling Kay
Published: January 2023

We prove the vanishing modulo torsion of the higher direct images of the sheaf of Witt vectors (and the Witt canonical sheaf) for a purely inseparable projective alteration between normal finite quotients over a perfect field. For this, we show that the relative Hodge-Witt cohomology admits an action of correspondences. As an application we define Witt-rational singularities which form a broader class than rational singularities. In particular, finite quotients have Witt-rational singularities. In addition, we prove that the torsion part of the Witt vector cohomology of a smooth, proper scheme is a birational invariant.
Symplectic involutions of $K3$ surfaces act trivially on $\mathrm{CH}_0$
Authors: Voisin Claire
Published: January 2023

A symplectic involution on a

K3

surface is an involution which preserves the holomorphic 2-form. We prove that such a symplectic involution acts as the identity on the

CH_0

group of the

K3

surface, as predicted by Bloch's conjecture.
Bott periodicity for inclusions of symmetric spaces
Authors: Mare Augustin-Liviu , Quast Peter
Published: January 2023

When looking at Bott's original proof of his periodicity theorem for the stable homotopy groups of the orthogonal and unitary groups, one sees in the background a differential geometric periodicity phenomenon. We show that this geometric phenomenon extends to the standard inclusion of the orthogonal group into the unitary group. Standard inclusions between other classical Riemannian symmetric spaces are considered as well. An application to homotopy theory is also discussed.
Duality for $\Bbb Z$-constructible sheaves on curves over finite fields
Authors: Geisser Thomas
Published: January 2023

We prove a duality theorem for Weil-etale cohomology of

\Z

-constructible sheaves on curves over finite fields.
Coherence for weak units
Authors: Joyal André , Kock Joachim
Published: January 2023

We define weak units in a semi-monoidal 2-category

\mathcal C

as cancellable pseudo-idempotents: they are pairs

(I,\alpha)

where

I

is an object such that tensoring with

I

from either side constitutes a biequivalence of

\mathcal C

, and

\alpha: I \otimes I \to I

is an equivalence in

\mathcal C

. We show that this notion of weak unit has coherence built in: Theorem A:

\alpha

has a canonical associator 2-cell, which automatically satisfies the pentagon equation. Theorem B: every morphism of weak units is automatically compatible with those associators. Theorem C: the 2-category of weak units is contractible if non-empty. Finally we show (Theorem E) that the notion of weak unit is equivalent to the notion obtained from the definition of tricategory:

\alpha

alone induces the whole family of left and right maps (indexed by the objects), as well as the whole family of Kelly 2-cells (one for each pair of objects), satisfying the relevant coherence axioms.
A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a Riemann surface
Authors: Biswas Indranil
Published: January 2023

Let

E_G

be a holomorphic principal

G

-bundle over a compact connected Riemann surface, where

G

is a connected reductive affine algebraic group defined over

\ C

, such that

E_G

admits a holomorphic connection. Take any

\beta \in H^0(X, \operatorname{ad}(E_G))

, where

\operatorname{ad}(E_G)

is the adjoint vector bundle for

E_G

, such that the conjugacy class

\beta (x) \in {\mathfrak g}/G, x \in X

, is independent of

x

. We give a sufficient condition for the existence of a holomorphic connection on

E_G

such that

\beta

is flat with respect to the induced connection on

\operatorname{ad}(E_G)

.
Realizability and admissibility under extension of $p$-adic and number fields.
Authors: Neftin Danny , Vishne Uzi
Published: January 2023

A finite group

G

is

K

-admissible if there is a

G

-crossed product

K

-division algebra. In this manuscript we study the behavior of admissibility under extensions of number fields

M/K

. We show that in many cases, including Sylow metacyclic and nilpotent groups whose order is prime to the number of roots of unity in

M

, a

K

-admissible group

G

is

M

-admissible if and only if

G

satisfies the easily verifiable Liedahl condition over

M

.
On Zagier's conjecture for base changes of elliptic curves
Authors: Brunault François
Published: January 2023

Let

E

be an elliptic curve over Q, and let

F

be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjecture for

L(E_F,2)

, where

E_F

is the base change of

E

to

F

.
The magnitude of metric spaces
Authors: Leinster Tom
Published: January 2023

Magnitude is a real-valued invariant of metric spaces, analogous to Euler characteristic of topological spaces and cardinality of sets. The definition of magnitude is a special case of a general categorical definition that clarifies the analogies between cardinality-like invariants in mathematics. Although this motivation is a world away from geometric measure, magnitude, when applied to subsets of

{R}^n

, turns out to be intimately related to invariants such as volume, surface area, perimeter and dimension. We describe several aspects of this relationship, providing evidence for a conjecture (first stated in joint work with Willerton) that magnitude encodes all the most important invariants of classical integral geometry.
Convergence of Voevodsky's slice tower
Authors: Levine Marc
Published: January 2023

We consider Voevodsky's slice tower for a finite spectrum

\mathcal E

in the motivic stable homotopy category over a perfect field

k

. In case

k

has finite cohomological dimension, we show that the slice tower converges, in that the induced filtration on the bi-graded homotopy sheaves

\Pi_{a,b}f_n\mathcal E

is finite, exhaustive and separated at each stalk (after inverting the exponential characteristic of

k

). This partially verifies a conjecture of Voevodsky.
Reduced operator algebras of trace-preserving quantum automorphism groups
Authors: Brannan Michael
Published: January 2023

Let

B

be a finite dimensional C

^\ast

-algebra equipped with its canonical trace induced by the regular representation of

B

on itself. In this paper, we study various properties of the trace-preserving quantum automorphism group

\mathbb G

of

B

. We prove that the discrete dual quantum group

\widehat{\mathbb G}

has the property of rapid decay, the reduced von Neumann algebra

L^\infty(\mathbb G)

has the Haagerup property and is solid, and that

L^\infty(\mathbb G)

is (in most cases) a prime type II

_1

-factor. As applications of these and other results, we deduce the metric approximation property, exactness, simplicity and uniqueness of trace for the reduced

C^\ast

-algebra

C_r(\mathbb G)

, and the existence of a multiplier-bounded approximate identity for the convolution algebra

L^1(\mathbb G)

.
Holomorphic connections on filtered bundles over curves
Authors: Biswas Indranil , Heu Viktoria
Published: January 2023

Let

X

be a compact connected Riemann surface and

E_P

a holomorphic principal

P

-bundle over

X

, where

P

is a parabolic subgroup of a complex reductive affine algebraic group

G

. If the Levi bundle associated to

E_P

admits a holomorphic connection, and the reduction

E_P \subset E_P\times^P G

is rigid, we prove that

E_P

admits a holomorphic connection. As an immediate consequence, we obtain a sufficient condition for a filtered holomorphic vector bundle over

X

to admit a filtration preserving holomorphic connection. Moreover, we state a weaker sufficient condition in the special case of a filtration of length two.
A new approach to the geometric Satake equivalence
Authors: Richarz Timo
Published: January 2023

I give another proof of the geometric Satake equivalence from I. Mirkovic and K. Vilonen citeMV over a separably closed field. Over a not necessarily separably closed field, I obtain a canonical construction of the Galois form of the full

L

-group.
Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras
Authors: Koenig Steffen , Yang Dong
Published: January 2023

Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded

t

-structures with length heart and (4) bounded co-

t

-structures. These correspondences are shown to commute with mutations and partial orders. The results are valid for finite-dimensional algebras. A concrete example is given to illustrate how these correspondences help to compute the space of Bridgeland's stability conditions.
Prym-Tjurin constructions on cubic hypersurfaces
Authors: Shen Mingmin
Published: January 2023

In this paper, we give a Prym-Tjurin construction for the cohomology and the Chow groups of a cubic hypersurface. On the space of lines meeting a given rational curve, there is the incidence correspondence. This correspondence induces an action on the primitive cohomology and the primitive Chow groups. We first show that this action satisfies a quadratic equation. Then the Abel-Jacobi mapping induces an isomorphism between the primitive cohomology of the cubic hypersurface and the Prym-Tjurin part of the above action. This also holds for Chow groups with rational coefficients. All the constructions are based on a natural relation among topological (resp. algebraic) cycles on

X

modulo homological (resp. rational) equivalence.
Pulling apart 2-spheres in 4-manifolds
Authors: Schneiderman Rob , Teichner Peter
Published: January 2023

An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of emphnon-repeating Whitney towers. The accompanying higher-order intersection invariants provide a geometric generalization of Milnor's link-homotopy invariants, and can give the complete obstruction to pulling apart 2-spheres in certain families of 4-manifolds. It is also shown that in an arbitrary simply connected 4-manifold any number of parallel copies of an immersed 2-sphere with vanishing self-intersection number can be pulled apart, and that this is not always possible in the non-simply connected setting. The order 1 intersection invariant is shown to be the complete obstruction to pulling apart 2-spheres in any 4-manifold after taking connected sums with finitely many copies of

S^2\times S^2

; and the order 2 intersection indeterminacies for quadruples of immersed 2-spheres in a simply-connected 4-manifold are shown to lead to interesting number theoretic questions.