bluuebunny/crossref_metadata_2025 huggingface dataset:
Possible Employment and Career Development in the South African Cannabis Market
Authors: Khumalo Njabulo
Published: January 2023

The aim of the chapter is to provide knowledge on the opportunities that the cannabis market has for South Africa. It further provides new models developed from the current literature on the related subjects. The industry also plans to improve the current products, which requires a lot of training and development from the existing people in the market. Therefore, this chapter will cover a range of topics such as the employment relation act, entrepreneurship competencies, human resource planning, training and development, recommendable diversity and motivational models, national qualifications framework (NQF), as well as to look at the future jobs within the cannabis industry.
The Industrialization of Cannabis in South Africa
Authors: Vilakazi Mlondi B. F.
Published: January 2023

This chapter aims to understand the opportunities that are available for the industrialisation of cannabis in South Africa from the developmental state perspective. The exclusion of Black people in the economy is still the main theme of the South African economy 28 years into democracy. Therefore, the intersection between the state and its importance in terms of guiding the private sector to achieve industrialisation and redistribution is a theme worthy of exploring. Interestingly, cannabis being a nascent sector in the economy, can either create opportunities for inclusion of those previously excluded, or it could sustain the dominance of those who presently control the status quo. Hence to facilitate such inclusion the state needs to play a pivotal facilitative role. Therefore, three themes are the focus of this chapter: i) developmental state; ii) opportunity for the cannabis industry in South Africa; and iii) redistribution - what form of distribution is required to occur in the industry to benefit the entire South African population.
Editorial Note
Authors: Gnanapala W. A. K. C. , Cooper Malcolm , Dewasiri N. J.
Published: January 2023

No abstract available
Crevasse fillings and ablation slide moraines, Stopover Lake area, N.W.T.
Authors: Mackay J R
Published: January 2023

A complex pattern of crevasse fillings, eskers and ablation slide moraines resembling dead-ice landscape occurs in an area of 40 square miles in he vicinity of Stopover Lake, 80 miles north of Smith Arm, Great Bear Lake, N .W.T. Open fissures and crevasses of
stagnant ice appear to have received deposits of sediment which were transported into the area by a large river whose abandoned channel lies to the east of Stopover Lake. At the time of deposition the controlling water level was from 1,150 to 1,250 feet above sea level. F ollowing a rapid lowering
of the water level to below 1,150 feet, ablation slide moraines, which may be annual features, were formed by the chuting, sliding and slumping of ablation material clown the sicles of wasting ice-blocks left by the retreating ice front.
Study of hematological changes in patients with chronic renal failure undergoing hemodialysis (pre and post)
Authors: Das Purna Chandra , Ghosh Soma , Banerjee Uma
Published: January 2023

Background:

Chronic renal failure (CRF), a debilitating condition responsible for high morbidity and mortality considered a financial burden to the government and society. Determining the prevalence of CRF in any country is important for planning the care of affected patients.

Aim and Objectives:

The study aimed at looking for the hematological changes before, and following hemodialysis (HD) in CRF patients. The objectives included comparing complete hemogram, coagulation profile, and blood biochemistry before and after HD; determining hematological complications post-HD; taking precautions to reduce morbidity and mortality from hematological point of view; and assessing changes in hematological profile of CRF patients undergoing HD.

Materials and Methods:

An institutional cross-sectional study was done on 62 patients of CRF undergoing HD. The hematological and biochemical parameters were studied along with urinary findings.

Results:

Males were more affected in the study. The hematological parameters which were elevated following dialysis were total leukocyte count, erythrocyte sedimentation rate, hemoglobin, hematocrit, mean corpuscular volume, mean corpuscular hemoglobin (MCH), bleeding and clotting time, prothrombin time, activated partial thromboplastin time, but MCH concentration and platelet count showed a fall. Postprandial blood sugar, calcium and erythropoietin showed elevated levels following hemodialysis., while decreased levels were found in fasting blood sugar, sodium, potassium, phosphate, urea, and creatinine. Urinary studies showed a increase in specific gravity and a decrease in 24 h urinary protein.

Conclusion:

CRF is becoming a dreadful condition in society, with dialysis playing an eminent role in treatment modality. Formulating precautions before and after dialysis based on various hematological and biochemical parameters can help to reduce morbidity and mortality.
Anxiety and depressive symptoms in health-care workers managing COVID-19 patients
Authors: Sabu Joel , Nayak K. Priya , Chacko Joshua S. , Karintholil Aiswarya Roy
Published: January 2023

Background:

Health-care professionals managing the pandemic are at higher risk of developing psychological distress and posttraumatic stress symptoms. The study highlights the importance of evaluating mental health among health-care workers to improve efficiency at work and also proves to be a major step to prevent suicide among health-care workers.

Materials and Methods:

The authors conducted a cross-sectional questionnaire-based clinical study, using the Depression, Anxiety, and Stress Scale-21 to assess stress, anxiety, and depressive symptoms among doctors and nurses managing COVID-19 patients in Karnataka.

Results:

Of 233 participants, 3 (1.3%), 27 (11.6%), 15 (6.4%), and 159 (68.2%) participants were suffering from mild, moderate, severe, and extremely severe anxiety respectively; 17 (7.3%), 32 (13.7%), 21 (9%), and 131 (56.2%) are suffering from mild, moderate, severe, extremely severe depressive symptoms, respectively; 15 (6.4%), 19 (8.2%), 26 (11.2%), and 114 (48.9%) are suffering from mild, moderate, severe, and extremely severe stress, respectively. The study also showed that health-care workers who had faced an epidemic in the past were able to cope up with the change in a scenario as compared to those who had not in the past.

Conclusion:

The study shows the prevalence of stress, anxiety, and depressive symptoms in doctors and nurses. It also shows that people who had exposure to a pandemic in the past were able to cope up better with the situation.
Bilateral Poland anomalies with horseshoe kidney
Authors: Chakraborty Partha , Majumder Priti , Mondal Rahuldeb , Halder Pankaj
Published: January 2023

Poland syndrome (PS) is a rare congenital disorder characterized by ipsilateral syndactyly and unilateral hypoaplasia of the chest wall. It may also be accompanied by dextrocardia, vertebral deformities, and renal malformations such as undescended testes and pyelonephritis. The degree of intrathoracic visceral compression and chest wall involvement dictate the course of treatment. Surgical drainage is occasionally required to treat sepsis and chronic infection. We present the case of an 11-month-old infant who had bilateral PS, horseshoe kidneys, and right-sided hydronephrosis, which is quite a rare association as per existing literature.
Evaluation of Morphological Changes in Hepatic Parenchyma, Bile Ducts, and Hepatic Vasculature in Patients with Oriental Cholangiohepatitis using Ultrasonography
Authors: Ahmad Kazime Mir Junaid , Ashraf Obaid , Ilyas Mohd.
Published: January 2023

Objective:

The objective of this study is to study the morphological changes in hepatic parenchyma, to characterize the intra and extrahepatic ductal changes and to study the morphological changes in vasculature of the liver in patients with oriental cholangiohepatitits (OCH).

Materials and Methods:

All documented or newly diagnosed cases of OCH, referred to the department of radiodiagnosis and imaging from Departments of Surgical Gastroenterology and Medical Gastroenterology were evaluated by ultrasonography (USG) and color Doppler study. The dilatation of the intrahepatic as well as extra-hepatic ducts was noted. The morphological changes in the liver parenchyma as well as hepatic vasculature were studied.

Results:

USG showed calculi in 53 (98.1%) cases, ductal dilatation in 52 (96.3%), and worms within biliary ducts in 10 cases (18.5%). Among parenchymal changes, atrophy was seen in 9 cases (16.6%), space-occupying lesion was seen in seven cases (12.9%), and peri-portal echogenicity in 10 cases (18.5%). Significant association was found between atrophic segments and reduced/absent blood flow in the affected segmental portal venous branches.

Conclusion:

USG is the preferred primary examination. Further imaging depends on the USG findings, the patient's symptomatology, the clinical problems, and the intended mode of treatment.

Advances in Knowledge:

USG plays a pivotal role in the evaluation of oriental cholangiohepatitis in the low resource settings where higher modalities like MRI are not available, especially in the remote areas of developing countries, as it has high degree of accuracy in the diagnosis of OCH.
Current Treatment of Meniere's Disease
Authors: Swain Santosh Kumar
Published: January 2023

Meniere's disease (MD) is a morbid inner ear disease that manifests disabling symptoms such as episodic vertigo, tinnitus, and fullness in the ear, for which patients seek immediate medical attention. The treatment of disabling vertigo of patients with MD remains controversial. Endolymphatic hydrops of the inner ear is presently considered the pathophysiology for explaining the underlying mechanisms of MD. There are many therapeutic options for MD, but no one is considered a highly effective modality for the cure of the MD. The primary purpose of the medical treatment of MD is to treat his or her symptoms rather than disease. Betahistine and diuretics are usually effective medical treatments for controlling vertigo in MD. However, there is no proven medical therapy for hearing loss or evolution of the disease in MD. There are several reports in favor of intratympanic use of aminoglycosides for the control of vertigo. Endolymphatic sac decompression is a surgical treatment option in the case of medically intractable MD. Vestibular neurectomy and labyrinthectomy are two important surgical techniques for the treatment of disabling vertigo of MD, but these surgical procedures are associated with relatively higher surgical morbidity. Recently, treatment with chemical labyrinthectomy/transtympanic gentamycin injection and endolymphatic sac decompression have gained favor for MD because they have less invasive techniques and are associated with fewer risks and side effects. The objective of this review article is to discuss current treatment options for MD to relieve disabling symptoms of MD and so improving the quality of life.
On the dimension of a composition algebra
Authors: Rost Markus
Published: January 2023

The possible dimensions of a composition algebra are 1, 2, 4, or 8. We give a tensor categorical argument.
Permanence properties of the Baum-Connes conjecture
Authors: Chabert Jérôme , Echterhoff Siegfried
Published: January 2023

In this paper we study the stability of the Baum–Connes conjecture with coefficients under various natural operations on the groups. We show that the class of groups satisfying this conjecture is stable under taking subgroups, Cartesian products, and more generally, under certain group extensions. In particular, we show that a group satisfies the conjecture if it has an amenable normal subgroup such that the associated quotient group satisfies the conjecture. We also study a natural induction homomorphism between the topological K-theory of a subgroup

H

of

G

and the topological K-theory of

G

with induced coefficient algebra, and show that this map is always bijective. Using this, we are also able to present new examples of groups which satisfy the conjecture with trivial coefficients.
Lifting Galois representations and a conjecture of Fontaine and Mazur
Authors: Noot Rutger
Published: January 2023

Mumford has constructed 4-dimensional abelian varieties with trivial endomorphism ring, but whose Mumford–Tate group is much smaller than the full symplectic group. We consider such an abelian variety, defined over a number field

F

, and study the associated

p

-adic Galois representation. For

F

sufficiently large, this representation can be lifted to

\mathbf{G}_m(\mathbf{Q}_p)\times\mathrm{SL}_2(\mathbf{Q}_p)^3

. Such liftings can be used to construct Galois representations which are geometric in the sense of a conjecture of Fontaine and Mazur. The conjecture in question predicts that these representations should come from algebraic geometry. We confirm the conjecture for the representations constructed here.
Equivariant fiber polytopes
Authors: Reiner Victor
Published: January 2023

The equivariant generalization of Billera and Sturmfels' fiber polytope construction is described. This gives a new relation between the associahedron and cyclohedron, a different natural construction for the type B permutohedron, and leads to a family of order-preserving maps between the face lattice of the type B permutohedron and that of the cyclohedron
$L^2$-invariants of locally symmetric spaces
Authors: Olbrich Martin
Published: January 2023

Let

X=G/K

be a Riemannian symmetric space of the noncompact type,

\Gamma\subset G

a discrete, torsion-free, cocompact subgroup, and let

Y=\Gamma\backslash X

be the corresponding locally symmetric space. In this paper we explain how the Harish-Chandra Plancherel Theorem for

L^2(G)

and results on

({\mathfrak g}, K)

-cohomology can be used in order to compute the

L^2

-Betti numbers, the Novikov–Shubin invariants, and the

L^2

-torsion of

Y

in a uniform way thus completing results previously obtained by Borel, Lott, Mathai, Hess and Schick, Lohoue and Mehdi. It turns out that the behaviour of these invariants is essentially determined by the fundamental rank

m=\mathrm{rk}_{\Bbb C}G -\mathrm{rk}_{\Bbb C}K

of

G

. In particular, we show the nonvanishing of the

L^2

-torsion of

Y

whenever

m=1

.
Order of torsion in $\mathrm{CH}^4$ of quadrics
Authors: Karpenko Nikita A.
Published: January 2023

It is shown that the order of the torsion subgroup in the 4-codimensional Chow group

\mathrm{CH}^4(X_\varphi)

of a projective quadric

X_\varphi

is at most 4 provided that the dimension of the corresponding quadratic form

\varphi

is greater than 8.
Arithmetic characteristic classes of automorphic vector bundles
Authors: Burgos Gil José I. , Kramer Jürg , Kühn Ulf
Published: January 2023

We develop a theory of arithmetic characteristic classes of (fully decomposed) automorphic vector bundles equipped with an invariant hermitian metric. These characteristic classes have values in an arithmetic Chow ring constructed by means of differential forms with certain log-log type singularities. We first study the cohomological properties of log-log differential forms, prove a Poincaré lemma for them and construct the corresponding arithmetic Chow groups. Then, we introduce the notion of log-singular hermitian vector bundles, which is a variant of the good hermitian vector bundles introduced by Mumford, and we develop the theory of arithmetic characteristic classes. Finally we prove that the hermitian metrics of automorphic vector bundles considered by Mumford are not only good but also log-singular. The theory presented here provides the theoretical background which is required in the formulation of the conjectures of Maillot-Roessler in the semi-abelian case and which is needed to extend Kudla's program about arithmetic intersections on Shimura varieties to the non-compact case.
On the equivariant Tamagawa number conjecture for Abelian extensions of a quadratic imaginary field
Authors: Bley W.
Published: January 2023

Let

k

be a quadratic imaginary field,

p

a prime which splits in

k/\mathbb Q

and does not divide the class number

h_k

of

k

. Let

L

denote a finite abelian extension of

k

and let

K

be a subextension of

L/k

. In this article we prove the

p

-part of the Equivariant Tamagawa Number Conjecture for the pair

(h^0(\operatorname{Spec}(L)), \mathbb Z[\operatorname{Gal}(L/K)])

.
Acyclicity versus total acyclicity for complexes over noetherian rings
Authors: Iyengar Srikanth , Krause Henning
Published: January 2023

It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is equivalent, as a triangulated category, to the homotopy category of injective modules. Restricted to compact objects, this statement is a reinterpretation of Grothendieck's duality theorem. Using this equivalence it is proved that the (Verdier) quotient of the category of acyclic complexes of projectives by its subcategory of totally acyclic complexes and the corresponding category consisting of injective modules are equivalent. A new characterization is provided for complexes in Auslander categories and in Bass categories of such rings.
On the approximation numbers of large Toeplitz matrices
Authors: Böttcher A.
Published: January 2023

The

k

th approximation number

s_k^{(p)}(A_n)

of a complex

n \times n

matrix

A_n

is defined as the distance of

A_n

to the

n \times n

matrices of rank at most

n-k

. The distance is measured in the matrix norm associated with the

l^p

norm

(1<p<\infty)

on

\mathbf C^n

. In the case

p=2

, the approximation numbers coincide with the singular values.
Erratum to: Cohomology of arithmetic groups with infinite dimensional coefficient spaces
Authors: Deitmar Anton , Hilgert Joachim
Published: January 2023

A correction of an error in the proof of Lemma 5.3 is given.
Strictly convex drawings of planar graphs
Authors: Bárány Imre , Rote Günter
Published: January 2023

Every three-connected planar graph with

n

vertices has a drawing on an

O(n^2) \times O(n^2)

grid in which all faces are strictly convex polygons. These drawings are obtained by perturbing (not strictly) convex drawings on

O(n) \times O(n)

grids. Tighter bounds are obtained when the faces have fewer sides. In the proof, we derive an explicit lower bound on the number of primitive vectors in a triangle.
Motivic splitting lemma
Authors: Vishik A. , Zainoulline K.
Published: January 2023

Let

M

be a Chow motive over a field

F

. Let

X

be a smooth projective variety over

F

and

N

be a direct summand of the motive of

X

. Assume that over the generic point of

X

the motives

M

and

N

become isomorphic to a direct sum of twisted Tate motives. The main result of the paper says that if a morphism

f: M \to N

splits over the generic point of

X

then it splits over

F

, i.e.,

N

is a direct summand of

M

. We apply this result to various examples of motives of projective homogeneous varieties.
Maps onto certain Fano threefolds
Authors: Amerik Ekaterina
Published: January 2023

We prove that if

X

is a smooth projective threefold with

b_2=1

and

Y

is a Fano threefold with

b_2=1

, then for a non-constant map

f:X\rightarrow Y

, the degree of

f

is bounded in terms of the discrete invariants of

X

and

Y

. Also, we obtain some stronger restrictions on maps between certain Fano threefolds.
The minimum principle from a Hamiltonian point of view
Authors: Heinzner Peter
Published: January 2023

Let

G

be a complex Lie group and

G_\R

a real form of

G

. For a

G_\R

-stable domain of holomorphy

X

in a complex

G

-manifold we consider the question under which conditions the extended domain

G\cdot X

is a domain of holomorphy. We give an answer in term of

G_\R

-invariant strictly plurisubharmonic functions on

X

and the associate Marsden-Weinstein reduced space which is given by the Kaehler form and the moment map associated with the given strictly plurisubharmonic function. Our main application is a proof of the so called extended future tube conjecture which asserts that

G\cdot X

is a domain of holomorphy in the case where

X

is the

N

-fold product of the tube domain in

\mathbb C^4

over the positive light cone and

G

is the connected complex Lorentz group acting diagonally.
On the ground state energy of the translation invariant Pauli-Fierz model. II.
Authors: Barbaroux Jean-Marie , Vugalter Semjon A.
Published: January 2023

We determine the ground state energy of the translation invariant Pauli-Fierz model for an electron with spin, to subleading order

O(\alpha^2)

with respect to powers of the finestructure constant

\alpha

and prove rigorous error bounds of order

O(\alpha^3)

. A main objective of our argument is its brevity.
Stable maps and Chow groups
Authors: Huybrechts D. , Kemeny M.
Published: January 2023

According to the Bloch–Beilinson conjectures, an automorphism of a K3 surface

X

that acts as the identity on the transcendental lattice should act trivially on

\operatorname{CH}^2(X)

. We discuss this conjecture for symplectic involutions and prove it in one third of all cases. The main point is to use special elliptic K3 surfaces and stable maps to produce covering families of elliptic curves on the generic K3 surface that are invariant under the involution.
Integration of vector fields on smooth and holomorphic supermanifolds
Authors: Garnier Stéphane , Wurzbacher Tilmann
Published: January 2023

We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and extend these results to the case of holomorphic vector fields on complex supermanifolds. Furthermore we discuss local actions associated to super vector fields, and give several examples and applications, as, e.g., the construction of an exponential morphism for an arbitrary finite-dimensional Lie supergroup.
Global quadratic units and Hecke algebras
Authors: Hida Haruzo
Published: January 2023

Let

\{\rho_{\mathfrak p}\}_{\mathfrak p}

be a compatible system of two dimansional

{\mathfrak p}

-adic Galois representations attached to a cusp form of Neben type

\left({D\over }\right) (D>0)

. We shall give an exact criterion, in terms of the fundamental unit

\varepsilon

of

{\Bbb Q}(\sqrt{D})

, determining primes

{\mathfrak p}

for which the image of

\rho_{\mathfrak p}\mod{\mathfrak p}

is dihedral. Then we shall state a conjecture which gives an explicit description of the universal

p

-ordinary deformation ring of such mod

{\mathfrak p}

dihedral representations.
The perturbed Maxwell operator as pseudodifferential operator
Authors: De Nittis Giuseppe , Lein Max
Published: January 2023

As a first step to deriving effective dynamics and ray optics, we prove that the perturbed periodic Maxwell operator in

d = 3

can be seen as a pseudo­differential operator. This necessitates a better understanding of the periodic Maxwell operator

\mathbf M_0

. In particular, we characterize the behavior of

\mathbf M_0

and the physical initial states at small crystal momenta

k

and small frequencies. Among other things, we prove that generically the band spectrum is symmetric with respect to inversions at

k = 0

and that there are exactly 4 ground state bands with approximately linear dispersion near

k = 0

.
$\Bbb Z_{2}$-indices and factorization properties of odd symmetric Fredholm operators
Authors: Schulz-Baldes Hermann
Published: January 2023

A bounded operator

T

on a separable, complex Hilbert space is said to be odd symmetric if

I^*T^{t}I=T

where

I

is a real unitary satisfying

I^{2}=-1

and

T

^t denotes the transpose of

T

. It is proved that such an operator can always be factorized as

T=I^*A^{t}IA

with some operator

A

. This generalizes a result of Hua and Siegel for matrices. As application it is proved that the set of odd symmetric Fredholm operators has two connected components labelled by a

Z

_2-index given by the parity of the dimension of the kernel of

T

. This recovers a result of Atiyah and Singer. Two examples of

Z

_2-valued index theorems are provided, one being a version of the Noether-Gohberg-Krein theorem with symmetries and the other an application to topological insulators.
Decomposable cycles and Noether-Lefschetz loci
Authors: O'Grady Kieran G.
Published: January 2023

We prove that there exist smooth surfaces of degree

d

in

\mathbb P^3

whose group of rational equivalence classes of decomposable 0-cycles has rank at least

\lfloor \frac{d-1}3\rfloor

.
On rational and periodic solutions of stationary KdV equations
Authors: Weikard R.
Published: January 2023

Stationary solutions of higher order KdV equations play an important role for the study of the KdV equation itself. They give rise to the coefficients of the associated Lax pair

(P,L)

for which

P

and

L

have an algebraic relationship (and are therefore called algebro-geometric). This paper gives a sufficient condition for rational and simply periodic functions which are bounded at infinity to be algebro-geometric as those potentials of

L

for which

Ly=zy

has only meromorphic solutions. It also gives a new elementary proof that this is a necessary condition for any meromorphic function to be algebro-geometric.
Picard Groups, Weight Structures, and (noncommutative) Mixed Motives
Authors: Bondarko Mikhail , Tabuada Gonçalo
Published: January 2023

We develop a general theory which, under certain assumptions, enables the computation of the Picard group of a symmetric monoidal triangulated category equipped with a weight structure in terms of the Picard group of the associated heart. As an application, we compute the Picard group of several categories of motivic nature – mixed Artin motives, mixed Artin–Tate motives, bootstrap motivic spectra, noncommutative mixed Artin motives, noncommutative mixed motives of central simple algebras – as well as the Picard group of certain derived categories of symmetric ring spectra.
Modular Equalities for Complex Reflection Arrangements
Authors: Mačinic Anca Daniela , Papadima Ştefan , Popescu Clement Radu
Published: January 2023

We compute the combinatorial Aomoto-Betti numbers

\beta_{p}(\mathcal A)

of a complex reflection arrangement. When

\mathcal A

has rank at least 3, we find that

\beta_{p}(\mathcal A)\leq 2

, for all primes

p

. Moreover,

\beta_{p}(\mathcal A)=0

if

p>3

, and

\beta_{2}(\mathcal A)\neq 0

if and only if

\mathcal A

is the Hesse arrangement. We deduce that the multiplicity

e_{d}(\mathcal A)

of an order

d

eigenvalue of the monodromy action on the first rational homology of the Milnor fiber is equal to the corresponding Aomoto-Betti number, when

d

is prime. We give a uniform combinatorial characterization of the property

e_{d}(\mathcal A)\neq 0

, for

2\leq d\leq 4

. We completely describe the monodromy action for full monomial arrangements of rank 3 and 4. We relate

e_{d}(\mathcal A)

and

\beta_{p}(\mathcal A)

to multinets, on an arbitrary arrangement.
Overconvergent Modular Forms and Perfectoid Shimura Curves
Authors: Chojecki Przemysław , Hansen D. , Johansson C.
Published: January 2023

We give a new construction of overconvergent modular forms of arbitrary weights, defining them in terms of functions on certain affinoid subsets of Scholze's infinite-level modular curve. These affinoid subsets, and a certain canonical coordinate on them, play a role in our construction which is strongly analogous with the role of the upper half-plane and its coordinate '

z

' in the classical analytic theory of modular forms. As one application of these ideas, we define and study an overconvergent Eichler-Shimura map in the context of compact Shimura curves over

\Bbb{Q}

, proving stronger analogues of results of Andreatta-Iovita-Stevens.
Limit Linear Series on Chains of Elliptic Curves and Tropical Divisors on Chains of Loops
Authors: López Martín Alberto , Teixidor i Bigas Montserrat
Published: January 2023

We describe the space of Eisenbud-Harris limit linear series on a chain of elliptic curves and compare it with the theory of divisors on tropical chains. Either model allows to compute some invariants of Brill-Noether theory using combinatorial methods. We introduce effective limit linear series.
Abelian varieties for function fields of curves over local fields
Authors: Izquierdo Diego
Published: January 2023

Let

K

be the function field of a smooth projective curve

X

over a

p

-adic field or over

\Bbb C((t))

. We define Tate-Shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of

K

coming from a closed point of

X

. We prove arithmetic duality theorems for Tate-Shafarevich groups of abelian varieties over

K

.
On the Invertibility of Motives of Affine Quadrics
Authors: Bachmann Tom
Published: January 2023

We show that the reduced motive of a smooth affine quadric is invertible as an object of the triangulated category of motives

\bold{DM}(k,\Bbb Z[1/e])

(where

k

is a perfect field of exponential characteristic

e

). We also establish a motivic version of the conjectures of Po Hu on products of certain affine Pfister quadrics. Both of these results are obtained by studying a novel conservative functor on (a subcategory of)

\bold{DM}(k,\Bbb Z[1/e])

, the construction of which constitutes the main part of this work.
Potentially Crystalline Lifts of Certain Prescribed Types
Authors: Gee Toby , Herzig Florian , Liu Tong , Savitt David
Published: January 2023

We prove several results concerning the existence of potentially crystalline lifts of prescribed Hodge-Tate weights and inertial types of a given representation

\overline{r}:G_{K}\to\mathrm{GL}_{n}(\overline{\Bbb{F}}_p)

, where

K/\Bbb Q_p

is a finite extension. Some of these results are proved by purely local methods, and are expected to be useful in the application of automorphy lifting theorems. The proofs of the other results are global, making use of automorphy lifting theorems.
The Chern classes modulo $p$ of a regular representation
Authors: Kahn Bruno
Published: January 2023

Let

G

be a finite group and

\rho

a complex linear representation of

G

. In 1961, Atiyah and Venkov independently defined Chern classes

c_i(\rho)

with values in the integral or mod

p

cohomology of

G

. We consider here the mod

p

Chern classes of the regular representation

r_G

of

G

. Venkov claimed that

c_i(r_G)=0

for

i<p^n-p^{n-1}

, where

p^n

is the highest power of

p

dividing

|G|

; however his proof is only valid for

G

elementary abelian. In this note, we show Venkov's assertion is valid for any

G

. The proof also shows that the

c_i(r_G)

are

p

-powers of cohomology classes invariant by

Aut(G)

as soon as

G

is a non-abelian

p

-group.
Variety of Power Sums and Divisors in the Moduli Space of Cubic Fourfolds
Authors: Ranestad Kristian , Voisin Claire
Published: January 2023

We show that a cubic fourfold

F

that is apolar to a Veronese surface has the property that its variety of power sums

VSP(F,10)

is singular along a

K3

surface of genus 20 which is the variety of power sums of a sextic curve. This relates constructions of Mukai and Iliev and Ranestad. We also prove that these cubics form a divisor in the moduli space of cubic fourfolds and that this divisor is not a Noether-Lefschetz divisor. We use this result to prove that there is no nontrivial Hodge correspondence between a very general cubic and its

VSP

.
Log Abelian Varieties over a Log Point
Authors: Zhao Heer
Published: January 2023

We study (weak) log abelian varieties with constant degeneration in the log flat topology. If the base is a log point, we further study the endomorphism algebras of log abelian varieties. In particular, we prove the dual short exact sequence for isogenies, Poincaré complete reducibility theorem for log abelian varieties, and the semi-simplicity of the endomorphism algebras of log abelian varieties.
Commutative Algebraic Groups up to Isogeny
Authors: Brion Michel
Published: January 2023

Consider the abelian category

\mathcal{C}_k

of commutative group schemes of finite type over a field

k

. By results of Serre and Oort,

\mathcal{C}_k

has homological dimension 1 (resp. 2) if

k

is algebraically closed of characteristic 0 (resp. positive). In this article, we explore the abelian category of commutative algebraic groups up to isogeny, defined as the quotient of

\mathcal{C}_k

by the full subcategory

\mathcal{F}_k

of finite

k

-group schemes. We show that

\mathcal{C}_k/\mathcal{F}_k

has homological dimension 1, and we determine its projective or injective objects. We also obtain structure results for

\mathcal{C}_k/\mathcal{F}_k

, which take a simpler form in positive characteristics.
Limiting Absorption Principle for Schrödinger Operators with Oscillating Potentials
Authors: Jecko Thierry , Mbarek Aiman
Published: January 2023

Making use of the localised Putnam theory developed in [gj], we show the limiting absorption principle for Schrödinger operators with perturbed oscillating potential on appropriate energy intervals. We focus on a certain class of oscillating potentials (larger than the one in [GJ2]) that was already studied in [BD, DMR, DR1, DR2, MU, ReT1, ReT2]. Allowing long-range and short-range components and local singularities in the perturbation, we improve known results. A subclass of the considered potentials actually cannot be treated by the Mourre commutator method with the generator of dilations as conjugate operator. Inspired by [FH], we also show, in some cases, the absence of positive eigenvalues for our Schrödinger operators.
On the automorphic atoms of length 2 of $\mathrm{GL}_2(\mathbb{Q}_p)$
Authors: Morra Stefano
Published: January 2023

Let

p>3

be a prime. The aim of this paper is to give a description of the invariant space, under principal and Iwahori congruence subgroups of arbitrary level, of extensions of generic principal series representations appearing in the

p

-modular local Langlands correspondence for

\bold{GL}_2(\bold{Q}_p)

. As an application we describe Hecke isotypical components of the mod

p

cohomology of the modular curve over

\bold{Q}

with deeply ramified level at

p

.
Free Actions of Compact Quantum Groups on Unital $C^\ast$-Algebras
Authors: Baum Paul F. , De Commer Kenny , Hajac Piotr M.
Published: January 2023

Let

F

be a field,

\Gamma

a finite group, and

\mathrm{Map}(\Gamma,F)

the Hopf algebra of all set-theoretic maps

\Gamma\rightarrow F

. If

E

is a finite field extension of

F

and

\Gamma

is its Galois group, the extension is Galois if and only if the canonical map

E\otimes_FE\rightarrow E\otimes_F\mathrm{Map}(\Gamma,F)

resulting from viewing

E

as a

\mathrm{Map}(\Gamma,F)

-comodule is an isomorphism. Similarly, a finite covering space is regular if and only if the analogous canonical map is an isomorphism. In this paper, we extend this point of view to actions of compact quantum groups on unital

C^\ast

-algebras. We prove that such an action is free if and only if the canonical map (obtained using the underlying Hopf algebra of the compact quantum group) is an isomorphism. In particular, we are able to express the freeness of a compact Hausdorff topological group action on a compact Hausdorff topological space in algebraic terms. As an application, we show that a field of free actions on unital

C^\ast

-algebras yields a global free action.
Topological Conjugacy of Topological Markov Shifts and Cuntz–Krieger Algebras
Authors: Matsumoto Kengo
Published: January 2023

For an irreducible non-permutation matrix

A

, the triplet

(\mathcal{O}_A,\mathcal{D}_A,\rho^A)

for the Cuntz–Krieger algebra

\mathcal{O}_A

, its canonical maximal abelian

C^\ast

-subalgebra

\mathcal{D}_A

, and its gauge action

\rho^A

is called the Cuntz–Krieger triplet. We introduce a notion of strong Morita equivalence in the Cuntz–Krieger triplets, and prove that two Cuntz–Krieger triplets

(\mathcal{O}_A,\mathcal{D}_A,\rho^A)

and

(\mathcal{O}_B,\mathcal{D}_B,\rho^B)

are strong Morita equivalent if and only if

A

and

B

are strong shift equivalent. We also show that the generalized gauge actions on the stabilized Cuntz–Krieger algebras are cocycle conjugate if the underlying matrices are strong shift equivalent. By clarifying K-theoretic behavior of the cocycle conjugacy, we investigate a relationship between cocycle conjugacy of the gauge actions on the stabilized Cuntz–Krieger algebras and topological conjugacy of the underlying topological Markov shifts.
Lie Groups in Quasi-Poisson Geometry and Braided Hopf Algebras
Authors: Ševera Pavol , Valach Fridrich
Published: January 2023

We extend the notion of Poisson-Lie groups and Lie bialgebras from Poisson to

\frak{g}

-quasi-Poisson geometry and provide a quantization to braided Hopf algebras in the corresponding Drinfeld category. The basic examples of these

\frak{g}

-quasi-Poisson Lie groups are nilpotent radicals of parabolic subgroups. We also provide examples of moment maps in this new context coming from moduli spaces of flat connections on surfaces.
Iwasawa Theory and $F$-Analytic Lubin-Tate $(\varphi,\Gamma)$-Modules
Authors: Berger Laurent , Fourquaux Lionel
Published: January 2023

Let

K

be a finite extension of

\bold{Q}p

. We use the theory of

(\varphi,\Gamma)

-modules in the Lubin-Tate setting to construct some corestriction-compatible families of classes in the cohomology of

V

, for certain representations

V

of

\mathrm{Gal}(\bold{\bar{Q}}/K)

. If in addition

V

is crystalline, we describe these classes explicitly using Bloch-Kato's exponential maps. This allows us to generalize Perrin-Riou's period map to the Lubin-Tate setting.
Why do Solutions of the Maxwell-Boltzmann Equation Tend to be Gaussians? A Simple Answer
Authors: Hundertmark Dirk , Lee Young-Ran
Published: January 2023

The Maxwell-Boltzmann functional equation has recently attraction renewed interest since besides its importance in Boltzmann's kinetic theory of gases it also characterizes maximizers of certain bilinear estimates for solutions of the free Schrödinger equation. In this note we give a short and simple proof that, under some mild growth restrictions, any measurable complex-valued solution of the Maxwell-Boltzmann equation is a Gaussian. This covers most, if not all, of the applications.
Singularities of Moduli of Curves with a Universal Root
Authors: Galeotti Mattia
Published: January 2023

In a series of recent papers, Chiodo, Farkas and Ludwig carry out a deep analysis of the singular locus of the moduli space of stable (twisted) curves with an

\ell

-torsion line bundle. They show that for

\ell\leq 6

and

\ell\ne 5

pluricanonical forms extend over any desingularization. This opens the way to a computation of the Kodaira dimension without desingularizing, as done by Farkas and Ludwig for

\ell=2

, and by Chiodo, Eisenbud, Farkas and Schreyer for

\ell=3

. Here we treat roots of line bundles on the universal curve systematically: we consider the moduli space of curves

C

with a line bundle

L

such that

L^{\otimes\ell}\cong \omega_C^{\otimes k}

. New loci of canonical and non-canonical singularities appear for any

k\not\in\ell\Bbb Z

and

\ell>2

, we provide a set of combinatorial tools allowing us to completely describe the singular locus in terms of dual graphs. We characterize the locus of non-canonical singularities, and for small values of

\ell

we give an explicit description.
The Universal Connection for Principal Bundles over Homogeneous Spaces and Twistor Space of Coadjoint Orbits
Authors: Biswas Indranil , Wong Michael Lennox
Published: January 2023

Given a holomorphic principal bundle

Q\longrightarrow X

, the universal space of holomorphic connections is a torsor

C_1(Q)

for

{ad}\, Q\otimes T^\ast X

such that the pullback of

Q

to

C_1(Q)

has a tautological holomorphic connection. When

X= G/P

, where

P

is a parabolic subgroup of a complex simple group

G

, and

Q

is the frame bundle of an ample line bundle, we show that

C_1(Q)

may be identified with

G/L

, where

L \subset P

is a Levi factor. We use this identification to construct the twistor space associated to a natural hyper-Kähler metric on

T^\ast(G/P)

, recovering Biquard's description of this twistor space, but employing only finite-dimensional, Lie-theoretic means.
Essential Dimension in Mixed Characteristic
Authors: Brosnan Patrick , Reichstein Zinovy , Vistoli Angelo
Published: January 2023

Let

G

be a finite group, and let

R

be a discrete valuation ring with residue field

k

and fraction field

K

. We say that

G

is weakly tame at a prime

p

if it has no non-trivial normal

p

-subgroups. By convention, every finite group is weakly tame at

0

. We show that if

G

is weakly tame at char(k), then

\operatorname{ed}_K(G) \geq \operatorname{ed}_k(G)

. Here

\operatorname{ed}_F(G)

denotes the essential dimension of

G

over the field

F

. We also prove a more general statement of this type, for a class of étale gerbes

\mathcal{X}

over

R

. As a corollary, we show that if

G

is weakly tame at

p

, then

\operatorname{ed}_{L} G \geq \operatorname{ed}_{k} G

for any field

L

of characteristic

0

and any field

k

of characteristic

p

, provided that

k

contains

\overline {\mathbb{F}}_{p}

. We also show that a conjecture of A. Ledet asserting that

\operatorname{ed}_k \mathbb{Z}/p^n \mathbb{Z}) = n

for a field

k

of characteristic

p>0

implies that

\operatorname{ed}_{\mathbb{C}}(G) \geq n

for any finite group

G

which is weakly tame at

p

and contains an element of order

p^n

. To the best of our knowledge, an unconditional proof of the last inequality is out of the reach of all presently known techniques.
Categorically Morita Equivalent Compact Quantum Groups
Authors: Neshveyev Sergey , Yamashita Makoto
Published: January 2023

We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital

\mathrm{C}^\ast

-algebra endowed with commuting actions of two compact quantum groups corresponds to a bimodule category over their representation categories. We show that this bimodule category is invertible if and only if the actions are free, with finite dimensional fixed point algebras, which are in duality as Frobenius algebras in an appropriate sense. This extends the well-known characterization of monoidal equivalence in terms of bi-Hopf-Galois objects.
The automorphism group of linear sections of the Grassmannians $\Bbb G (1,N)$
Authors: Piontkowski J. , Van de Ven A.
Published: January 2023

The Grassmannians of lines in projective

N

-space,

\mathbb G(1,N)

, are embedded by way of the Plücker embedding in the projective space

\mathbb P(\bigwedge^2\mathbb C^{N+1})

. Let

H^l

be a general

l

-codimensional linear subspace in this projective space.

We examine the geometry of the linear sections

\mathbb G(1, N)\cap H^l

by studying their automorphism groups and list those which are homogeneous or quasihomogeneous.
Non-Koszulness of Operads and Positivity of Poincaré Series
Authors: Dotsenko Vladimir , Markl Martin , Remm Elisabeth
Published: January 2023

We prove that the operad of mock partially associative

n

-ary algebras is not Koszul, as conjectured by the second and the third author in 2009, and utilise the Zeilberger's algorithm for hypergeometric summation to demonstrate that non-Koszulness of that operad for

n=8

cannot be established by hunting for negative coefficients in the inverse of its Poincaré series.
On Semicontinuity of Multiplicities in Families
Authors: Smirnov Ilya
Published: January 2023

This paper investigates the behavior of Hilbert-Samuel multiplicity and Hilbert-Kunz multiplicity in families of ideals. We show that Hilbert-Samuel multiplicity is upper semicontinuous and that Hilbert-Kunz multiplicity is upper semicontinuous in families of finite type. As a consequence, F-rational signature, an invariant defined by Hochster and Yao as the infimum of relative Hilbert-Kunz multiplicities, is, in fact, a minimum. This gives a different proof for its main property: F-rational signature is positive if and only if the ring is F-rational. The tools developed in this paper can be also applied to families over

\mathbb{Z}

and yield a solution to Claudia Miller's question on reduction mod

p

of Hilbert-Kunz function.
Pure Projective Tilting Modules
Authors: Bazzoni Silvana , Herzog Ivo , Příhoda Pavel , Šaroch Jan , Trlifaj Jan
Published: January 2023

Let

T_R

be a

1

-tilting module with tilting torsion pair

(\operatorname{Gen} T, \mathcal{F})

in

\text{Mod}\text{-}R.

The following conditions are proved to be equivalent:

(1) T

is pure projective;

(2) \operatorname{Gen} T

is a definable subcategory of

\text{Mod}\text{-}R

with enough pure projectives; (3) both classes

\operatorname{Gen} T

and

\mathcal{F}

are finitely axiomatizable; and (4) the heart of the corresponding HRS

t

-structure (in the derived category

\mathcal{D}^b (\text{Mod}\text{-}R))

is Grothendieck. This article explores in this context the question raised by Saorín if the Grothendieck condition on the heart of an HRS

t

-structure implies that it is equivalent to a module category. This amounts to asking if

T

is tilting equivalent to a finitely presented module. This is resolved in the positive for a Krull-Schmidt ring, and for a commutative ring, a positive answer follows from a proof that every pure projective

1

-tilting module is projective. However, a general criterion is found that yields a negative answer to Saorín's Question and this criterion is satisfied by the universal enveloping algebra of a semisimple Lie algebra, a left and right noetherian domain.
Toric Sheaves on Hirzebruch Orbifolds
Authors: Wang Weikun
Published: January 2023

We provide a stacky fan description of the total space of certain split vector bundles, as well as their projectivization, over toric Deligne-Mumford stacks. We then specialize to the case of Hirzebruch orbifold

\mathcal{H}_r^{ab}

obtained by projectivizing

\mathcal{O} \oplus \mathcal{O}(r)

over the weighted projective line

\mathbb{P}(a,b)

. Next, we give a combinatorial description of toric sheaves on

\mathcal{H}_r^{ab}

and investigate their basic properties. With fixed choice of polarization and a generating sheaf, we describe the fixed point locus of the moduli scheme of

\mu

-stable torsion free sheaves of rank

1

and

2

on

\mathcal{H}_r^{ab}

. As an example, we obtain explicit formulas for generating functions of Euler characteristics of locally free sheaves of rank 2 on

\mathbb{P}(1,2) \times \mathbb{P}^1

.
A Horrocks-Type Theorem for Even Orthogonal $\text{K}_2$
Authors: Lavrenov Andrei V. , Sinchuk Sergei S.
Published: January 2023

We prove the Horrocks theorem for unstable even-dimensional orthogonal Steinberg groups. The Horrocks theorem for Steinberg groups is one of the principal ingredients needed for the proof of the

\text{K}_2

-analogue of Serre's problem, positive solution of which currently is only known in the linear case.