bluuebunny/crossref_metadata_2025_split huggingface dataset:
Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic
Authors: Bezrukavnikov Roman , Mirković Ivan , Rumynin Dmitriy 
Published: July 2016

In [BMR] we observed that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central character can be identified with coherent sheaves on the formal neighborhood of the corresponding (generalized) Springer fiber. In the present paper we treat singular central characters.The basic step is the Beilinson-Bernstein localization of modules with a fixed (generalized) central character λ as sheaves on the partial flag variety corresponding to the singularity of λ. These sheaves are modules over a sheaf of algebras which is a version of twisted crystalline differential operators. We discuss translation functors and intertwining functors. The latter generate an action of the affine braid group on the derived category of modules with a regular (generalized) central character, which intertwines different localization functors. We also describe the standard duality on Lie algebra modules in terms of D-modules and coherent sheaves.
Averaging formula for Nielsen coincidence numbers
Authors: Kim Seung Won , Lee Jong Bum 
Published: July 2016

AbstractIn this paper we study the averaging formula for Nielsen coincidence numbers of pairs of maps(f,g): M→Nbetween closed smooth manifolds of the same dimension. Suppose that G is a normal subgroup of Π = π1(M) with finite index andHis a normal subgroup of Δ = π1(N) with finite index such thatThen we investigate the conditions for which the following averaging formula holdswhereis any pair of fixed liftings of (f, g). We prove that the averaging formula holds whenMandNare orientable infra-nilmanifolds of the same dimension, and whenM = Nis a non-orientable infra-nilmanifold with holonomy groupℤ2and (f, g) admits a pair of liftingson the nil-coveringofM.
m-Blocks Collections and Castelnuovo-mumford Regularity in multiprojective spaces
Authors: Costa L. , Miró-Roig R. M. 
Published: July 2016

AbstractThe main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on n-dimensional smooth projective varieties X with an n-block collection B which generates the bounded derived category To this end, we use the theory of n-blocks and Beilinson type spectral sequence to define the notion of regularity of a coherent sheaf F on X with respect to the n-block collection B. We show that the basic formal properties of the Castelnuovo-Mumford regularity of coherent sheaves over projective spaces continue to hold in this new setting and we compare our definition of regularity with previous ones. In particular, we show that in case of coherent sheaves on ℙn and for the n-block collection Castelnuovo-Mumford regularity and our new definition of regularity coincide. Finally, we carefully study the regularity of coherent sheaves on a multiprojective space ℙn1x…x ℙnr with respect to a suitable n1 +…+ nr-block collection and we compare it with the multigraded variant of the Castelnuovo-Mumford regularity given by Hoffman and Wang in [14].
Every Curve of Genus not Greater Than Eight Lies on a K3 Surface
Authors: Ide Manabu 
Published: July 2016

Let C be a smooth irreducible complete curve of genus g ≥ 2 over an algebraically closed field of characteristic 0. An ample K3 extension of C is a K3 surface with at worst rational double points which contains C in the smooth locus as an ample divisor.In this paper, we prove that all smooth curve of genera. 2 ≤ g ≤ 8 have ample K3 extensions. We use Bertini type lemmas and double coverings to construct ample K3 extensions.
A Reduction Theorem for Stable sets of Holomorphic Foliations on Complex Tori
Authors: Ohsawa Takeo 
Published: July 2016

AbstractSome complex n-tori admit holomorphic foliations of codimension one besides the flat ones. It will be shown that such nonlinear foliations, possibly with singularities, can be reduced to those on 2-tori under some topological conditions. A crucial step is an application of the Hodge theory on pseudoconvex manifolds.
Averaging Formula for Nielsen Numbers of Maps on Infra-Solvmanifolds of Type (R)
Authors: Lee Jong Bum , Lee Kyung Bai 
Published: July 2016

We prove that the averaging formula for Nielsen numbers holds for continuous maps on infra-solvmanifolds of type (R): Let M be such a manifold with holonomy group Ψ and let f: M → M be a continuous map. The averaging formula for Nielsen numbersis proved. This is a workable formula for the difficult number N(f).
Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori
Authors: Chinta Gautam , Jorgenson Jay , Karlsson Anders 
Published: July 2016

AbstractBy a discrete torus we mean the Cayley graph associated to a finite product of finite cycle groups with the generating set given by choosing a generator for each cyclic factor. In this article we examine the spectral theory of the combinatorial Laplacian for sequences of discrete tori when the orders of the cyclic factors tend to infinity at comparable rates. First, we show that the sequence of heat kernels corresponding to the degenerating family converges, after rescaling, to the heat kernel on an associated real torus. We then establish an asymptotic expansion, in the degeneration parameter, of the determinant of the combinatorial Laplacian. The zeta-regularized determinant of the Laplacian of the limiting real torus appears as the constant term in this expansion. On the other hand, using a classical theorem by Kirchhoff, the determinant of the combinatorial Laplacian of a finite graph divided by the number of vertices equals the number of spanning trees, called thecomplexity, of the graph. As a result, we establish a precise connection between the complexity of the Cayley graphs of finite abelian groups and heights of real tori. It is also known that spectral determinants on discrete tori can be expressed using trigonometric functions and that spectral determinants on real tori can be expressed using modular forms on general linear groups. Another interpretation of our analysis is thus to establish a link between limiting values of certain products of trigonometric functions and modular forms. The heat kernel analysis which we employ uses a careful study ofI-Bessel functions. Our methods extend to prove the asymptotic behavior of other spectral invariants through degeneration, such as special values of spectral zeta functions and Epstein-Hurwitz–type zeta functions.
Mean representation number of integers as the sum of primes
Authors: Bhowmik Gautami , Schlage-Puchta Jan-Christoph 
Published: July 2016

AbstractAssuming the Riemann hypothesis, we obtain asymptotic estimates for the mean value of the number of representations of an integer as a sum of two primes. By proving a corresponding Ω-term, we show that our result is essentially the best possible.
Kummer surfaces associated to (1, 2)-polarized abelian surfaces
Authors: Mehran Afsaneh 
Published: July 2016

AbstractThe aim of this paper is to describe the geometry of the generic Kummer surface associated to a (1, 2)-polarized abelian surface. We show that it is the double cover of a weak del Pezzo surface and that it inherits from the del Pezzo surface an interesting elliptic fibration with twelve singular fibers of typeI2.
Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero
Authors: Hoshi Yuichiro 
Published: July 2016

AbstractLetlbe a prime number. In this paper, we prove that the isomorphism class of anl-monodromically full hyperbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-louter Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to Mochizuki which asserts that the isomorphism class of an elliptic curve which does not admit complex multiplication over a number field is completely determined by the kernels of the natural Galois representations on the various finite quotients of its Tate module.
Stickelberger elements and Kolyvagin systems
Authors: Büyükboduk Kâzim 
Published: July 2016

AbstractIn this paper, we construct (many) Kolyvagin systems out of Stickelberger elements utilizing ideas borrowed from our previous work on Kolyvagin systems of Rubin-Stark elements. The applications of our approach are twofold. First, assuming Brumer’s conjecture, we prove results on the odd parts of the ideal class groups of CM fields which are abelian over a totally real field, and we deduce Iwasawa’s main conjecture for totally real fields (for totally odd characters). Although this portion of our results has already been established by Wiles unconditionally (and refined by Kurihara using an Euler system argument, when Wiles’s work is assumed), the approach here fits well in the general framework the author has developed elsewhere to understand Euler/Kolyvagin system machinery when the core Selmer rank isr &gt;1 (in the sense of Mazur and Rubin). As our second application, we establish a rather curious link between the Stickelberger elements and Rubin-Stark elements by using the main constructions of this article hand in hand with the “rigidity” of the collection of Kolyvagin systems proved by Mazur, Rubin, and the author.
Quantum (sln, ∧V n ) link invariant and matrix factorizations
Authors: Yonezawa Yasuyoshi 
Published: July 2016

AbstractIn this paper, we give a generalization of Khovanov-Rozansky homology. We define a homology associated to the quantum (sln, ∧Vn) link invariant, where∧Vnis the set of fundamental representations ofUq(sln). In the case of an oriented link diagram composed of[k, 1]-crossings, we define a homology and prove that the homology is invariant under Reidemeister II and III moves. In the case of an oriented link diagram composed of general[i,j]-crossings, we define a normalized Poincaré polynomial of homology and prove that the normalized Poincaré polynomial is a link invariant.
How not to prove the Alon-Tarsi conjecture
Authors: Stones Douglas S. , Wanless Ian M. 
Published: July 2016

AbstractThe sign of a Latin square is −1 if it has an odd number of rows and columns that are odd permutations; otherwise, it is +1. LetLEnandLonbe, respectively, the number of Latin squares of ordernwith sign +1 and −1. The Alon-Tarsi conjecture asserts thatLEn≠Lonwhennis even. Drisko showed thatLEp+1≢Lop+1(modp3) for primep≥ 3 and asked if similar congruences hold for orders of the formpk+ 1,p+ 3, orpq+ 1. In this article we show that ift≤n, thenLEn+1≢L0n+1(modt3) only ift = nandnis an odd prime, thereby showing that Drisko’s method cannot be extended to encompass any of the three suggested cases. We also extend exact computation ton≤ 9, discuss asymptotics forLo/LE, and propose a generalization of the Alon-Tarsi conjecture.
Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements
Authors: Dimca Alexandru 
Published: July 2016

AbstractThe order of the Milnor fiber monodromy operator of a central hyperplane arrangement is shown to be combinatorially determined. In particular, a necessary and sufficient condition for the triviality of this monodromy operator is given.It is known that the complement of a complex hyperplane arrangement is cohomologically Tate and, if the arrangement is defined over ℚ, has polynomial count. We show that these properties hold for the corresponding Milnor fibers if the monodromy is trivial.We construct a hyperplane arrangement defined over ℚ, whose Milnor fiber has a nontrivial monodromy operator, is cohomologically Tate, and has no polynomial count. Such examples are shown not to exist in low dimensions.
Fonctions zêtaℓ-modulaires
Authors: Mínguez Alberto 
Published: July 2016

AbstractLet F be a non-Archimedean locally compact field, of residual characteristicp,and let D be a finite-dimensional central division F-algebra. Letℓbe a prime number different fromp.In this article, generalizing the results of [GJ], we associate, to eachℓ-modular smooth irreducible representationπof GLm(D), two invariantsL(T,π), ε(T,π,ψ),whereTis an indeterminate andψis a nontrivial character of F.
Kulikov surfaces form a connected component of the moduli space
Authors: Chan Tsz On Mario , Coughlan Stephen 
Published: July 2016

AbstractWe show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type withpg= 0 andK2= 6. We also give a new description for these surfaces, extending ideas of Inoue. Finally, we calculate the bicanonical degree of Kulikov surfaces and prove that they verify the Bloch conjecture.
Estimates for F-jumping numbers and bounds for Hartshorne–Speiser–Lyubeznik numbers
Authors: Mustaţă Mircea , Zhang Wenliang 
Published: July 2016

AbstractGiven an ideal a on a smooth variety in characteristic zero, we estimate theF-jumping numbers of the reductions of a to positive characteristic in terms of the jumping numbers of a and the characteristic. We apply one of our estimates to bound the Hartshorne–Speiser–Lyubeznik invariant for the reduction to positive characteristic of a hypersurface singularity.
Algebras of acyclic cluster type: Tree type and type Ã
Authors: Amiot Claire , Oppermann Steffen 
Published: July 2016

AbstractIn this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of typeÃ.We are particularly interested in their derived equivalence classification. We prove that each algebra which is cluster equivalent to a tree quiver is derived equivalent to the path algebra of this tree. Then we describe explicitly the algebras of cluster typeÃnfor each possible orientation ofÃn.We give an explicit way to read off the derived equivalence class in which such an algebra lies, and we describe the Auslander-Reiten quiver of its derived category. Together, these results in particular provide a complete classification of algebras which are cluster equivalent to tame acyclic quivers.
Stability of tautological bundles on the Hilbert scheme of two points on a surface
Authors: Wandel Malte 
Published: July 2016

AbstractLet (X, H) be a polarized smooth projective surface satisfyingH1(Χ, OΧ) = 0, and letƑbe either a rank 1 torsion-free sheaf or a rank 2μH-stable vector bundle onΧ. Assume thatc1(Ƒ) ≠ 0. This article shows that the rank 2—respectively, rank 4—tautological sheafƑ[2]associated withƑon the Hilbert squareΧ[2]isμ-stable with respect to a certain polarization.
Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities
Authors: bona Jerry L. , Cohen Jonathan , Wang Gang 
Published: July 2016

AbstractIn this paper, coupled systemsof Korteweg-de Vries type are considered, whereu=u(x, t),v=v(x, t) are real-valued functions and wherex, t∈R. Here, subscripts connote partial differentiation andare quadratic polynomials in the variablesuandv. Attention is given to the pure initial-value problem in whichu(x, t) andv(x, t) are both specified att= 0, namely,forx∈ ℝ. Under suitable conditions onPandQ, global well-posedness of this problem is established for initial data in theL2-based Sobolev spacesHs(ℝ) ×Hs(ℝ) for anys&gt; ‒3/4.
New Formulation of the Axiom of Choice by making use of the Comprehension Operator
Authors: Ono Katuzi 
Published: July 2016

We have introduced in our former work [1] and [2] the comprehension operator “{·)”, which maps every binary relation to a binary relation. The definition of this operatoris remarkable in that it can be defined in any formal system having themembershiprelation ∈, which is hereafter called theuniversal systemand is denoted by U. In this work, we would like to point out that theaxiom of choice, in the strong sense as well as in the weak sense, can be formulated in an extremely simple style by making use of the comprehension operator.
Generalized Commutative Rings
Authors: Belluce L. P. , Herstein I. N. , Jain S. K. 
Published: July 2016

Among his various interests in algebra Nakayama also took part in the various researches, published in the early and middle 1950’s, which dealt with the commutativity of rings. This paper, which studies a problem of a related sort, thus seems appropriate in a Journal honoring his memory.We shall study a certain class of rings which satisfy a weak form of the commutative law and shall show that the structure of such rings can be determined.
A Characterization of QF-3 Rings
Authors: WU L. E. T. , Mochizuki H. Y. , Jans J. P. 
Published: July 2016

A left QF-3 ring R is one in which RR, the ring considered as a left module over itself, can be embedded in a projective infective left R module Q(RR). QF-3 rings were introduced by Thrall [14] and have been studied and characterized by a number of authors [5, 8, 9, 12, 13, 15] usually restricted to the case of algebras over a field. In such a case, the concept of left QF-3 and right QF-3 coincide.The study of QF-3 rings and algebras and many other such classes of rings had its origin in the now classic papers of Nakayama [10, 11]. He was an outstanding pioneer in algebra for many years, and we acknowledge our great debt to him and to his many excellent papers.
On the Cohomology of Some Hopf Algebras
Authors: Shimada Nobuo , Iwai Akira 
Published: July 2016

In this paper we study certain injective resolutions for some Hopf algebras. An injective resolution for a coalgebra A with augmentation η is defined to be such an exact sequence thatwhere K is the basic field, Xn are injective A-comodules and δn are morphism of A-comodules.
On Quasi-Linear Parabolic Equations
Authors: Ikeda Yoshiaki 
Published: July 2016

In this paper we consider the following quasi-linear parabolic equationsLu = ut — div A(x, t, u, ux)+B(x, t, u, ux= 0,where A is a given vector function of the variables x,t,u,uX, and B is a given scalar function of the some variables. We assume that they are difined in the rectangle
A Characterization of the Finite Simple Groups PSp(4,q), G2(q), D42(q), II
Authors: Fong Paul 
Published: July 2016

Our object in this paper is to prove the following result.THEOREM. Let G be a finite group satisfying the following conditions:(*) G has subgroups L1, L2 such that L1 ≃ SL(2, q1), L2 ≃ SL(2, q2), [L1 L2] = 1, , where j is an involution, and |C(j): L1L2| = 2.(**) where n2 = 1,
A Class of Riemannian Manifolds Satisfying R(X ,Y)·R = 0
Authors: Tanno Shûkichi 
Published: July 2016

Let (M,g) be a Riemannian manifold and let R be its Riemannian curvature tensor. If (M, g) is a locally symmetric space, we have(*)	R(X,Y)·R = 0 for all tangent vectors X,Ywhere the endomorphism R(X,Y) (i.e., the curvature transformation) operates on R as a derivation of the tensor algebra at each point of M. There is a question: Under what additional condition does this algebraic condition (*) on R imply that (M,g) is locally symmetric (i.e., ∇R = 0)? A conjecture by K. Nomizu [5] is as follows : (*) implies ∇R = 0 in the case where (M, g) is complete and irreducible, and dim M ≥ 3. He gave an affirmative answer in the case where (M,g) is a certain complete hypersurface in a Euclidean space ([5]).
Vector Bundles on an Elliptic Curve
Authors: Oda Tadao 
Published: July 2016

Let k be an algebraically closed field of characteristic p≧ 0, and let X be an abelian variety over k.The goal of this paper is to answer the following questions, when dim(X) = 1 and p≠0, posed by R. Hartshorne:
(1)Is E(P) indecomposable, when E is an indecomposable vector bundle on X?(2)Is the Frobenius map F*: H1 (X, E) → H1 (X, E(p)) injective?We also partly answer the following question posed by D. Mumford:(3)Classify, or at least say anything about, vector bundles on X when dim (X) > 1.
Oscillation Function of a Multiparameter Gaussian Process
Authors: Jain Naresh C. , Kallianpur G. 
Published: July 2016

AbstractIt is our object in this paper to show that the recent results of K. Ito and M. Nisio [4] on the oscillation function of Gaussian processes on [0,1] are valid for Gaussian processes with a general multiparameter “time” set T. Except in extending Theorem 4 of [4] where we assume T to be the d-dimensional cube, in all other cases we allow T to be a separable metric space. Despite the generality of the time set, the proofs are achieved essentially using the method of the above mentioned authors. However, in Theorem 1 below we find the use of Lemma 6 of [5] more convenient than the approach via orthogonal expansions and Kolmogorov’s zero-one law as is done in [4].
Cores of Potential Operators for Processes With Stationary Independent Increments
Authors: Sato Ken-Iti 
Published: July 2016

Let Xt(ω)) be a stochastic process with stationary independent increments on the N-dimensional Euclidean space RN, right continuous in t ≧ 0 and starting at the origin. Let C0(RN) be the Banach space of real-valued continuous functions on RN vanishing at infinity with norm . The process induces a transition semigroup of operators Tt on C0(RN) :Ttf(x) = Ef(x + Xt).
Stable vector bundles on an algebraic surface
Authors: Maruyama Masaki 
Published: July 2016

Let X be a non-singular projective algebraic curve over an algebraically closed field k. D. Mumford introduced the notion of stable vector bundles on X as follows;DEFINITION ([7]). A vector bundle E on X is stable if and only if for any non-trivial quotient bundle F of E,where deg ( • ) denotes the degree of the first Chern class of a vector bundles and r( • ) denotes the rank of a vector bundle.
On an Existence Lemma in Valuation Theory
Authors: Nagata Masayoshi , Nakayama Tadasi , Tuzuku Tosiro 
Published: July 2016

Recently one of the writers used, in proving a theorem on the commutativity of certain division rings, the following lemma :I. Let L be a field and K be its proper subfield. Except either when L is of characteristic p ≠ O and absolutely algebraic or ivhen L is algebraic and purely inseparable over K, there exists a pair of distinct (special exponential) valuations in L which coincide on K.II. Let K be a field which is either of characteristic 0 or not absolutely algebraic, and L be its separable finite extension. There exist then infinitely many valutions in L which are of 1st degree over K.
Some relations between differential geometric invariants and topological invariants of submanifolds
Authors: Chen Bang-Yen 
Published: July 2016

Let M be an n-dimensional manifold immersed in an m-dimensional euclidean space Em and let ∇ and ∇̃ be the covariant differentiations of M and Em, respectively. Let X and Y be two tangent vector fields on M. Then the second fundamental form h is given by(1.1) ∇̃XY = ∇XY + h(X,Y).
Congruences between cusp forms and linear representations of the Galois group
Authors: Koike Masao 
Published: July 2016

Let f(z) be a cusp form of type (l,ε) on Γ0(N) which is a common eigenfunction of all Hecke operators. For such f(z), Deligne and Serre [1] proved that there exists a linear representationsuch that the Artin L-function for p is equal to the L-function associated to f(z).
C3-Actions and algebraic threefolds with ample tangent bundle
Authors: Mabuchi Toshiki 
Published: July 2016

One of the most challenging problems in complex differential geometry is the following conjecture of Frankel [3].(F-n) A compact Kaehler manifold M of dimension n with positive sectional (or more generally, positive holomorphic bisectional) curvature is biholomorphic to the complex projective space Pn(C).
Distance functions and umbilic submanifolds of hyperbolic space
Authors: Cecil Thomas E. , Ryan Patrick J. 
Published: July 2016

In 1972, Nomizu and Rodriguez [5] found the following characterization of the complete umbilic submanifolds of Euclidean space.Theorem A. Let Mn, n ≥ 2, be a connected, complete Riemannian manifold isometrically immersed in a Euclidean space Em. Every Morse function of the form Lp has index 0 or n at all of its critical points if and only if Mnis embedded as a Euclidean n-subspace or a Euclidean n-sphere in Em.