Brauer's theorem on induced characters
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The marked Brauer category Open
We introduce the marked Brauer algebra and the marked Brauer category. These\ngeneralize the analogous constructions for the ordinary Brauer algebra to the\nsetting of a homogeneous bilinear form on a $\\mathbb{Z}_2$-graded vector space.\n…
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Comparing descent obstruction and Brauer-Manin obstruction for open varieties Open
International audience
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Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties Open
It is well known that the category of quasi-coherent sheaves on a gerbe banded by a diagonalizable group decomposes according to the characters of the group. We establish the corresponding decomposition of the unbounded derived category of…
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Comparing descent obstruction and Brauer-Manin obstruction for open varieties Open
We provide a relation between Brauer-Manin obstruction and descent obstruction for torsors over open varieties under a connected linear algebraic group or a group of multiplicative type is given. Such a relation is further refined for tors…
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Kummer varieties and their Brauer groups Open
We study Kummer varieties attached to 2-coverings of abelian varieties of arbitrary dimension. Over a number field we show that the subgroup of odd order elements of the Brauer group does not obstruct the Hasse principle. Sufficient condit…
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The simplicial complex of Brauer pairs of a finite reductive group Open
In this paper we study the simplicial complex induced by the poset of Brauer pairs ordered by inclusion for the family of finite reductive groups. In the defining characteristic case the homotopy type of this simplicial complex coincides w…
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Brauer characters of $q’$- degree Open
We show that if $p$ is a prime and $G$ is a finite $p$-solvable group satisfying the condition that a prime $q$ divides the degree of no irreducible $p$-Brauer character of $G$, then the normalizer of some Sylow $q$-subgroup of $G$ meets a…
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Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications Open
In this article we construct three explicit natural subgroups of the\nBrauer-Picard group of the category of representations of a\nfinite-dimensional Hopf algebra. In examples the Brauer Picard group decomposes\ninto an ordered product of …
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A NOTE ON -PARTS OF BRAUER CHARACTER DEGREES Open
Let $G$ be a finite group and $p$ be an odd prime. We show that if $\mathbf{O}_{p}(G)=1$ and $p^{2}$ does not divide every irreducible $p$ -Brauer character degree of $G$ , then $|G|_{p}$ is bounded by $p^{3}$ when $p\geqslant 5$ or $p=3$ …
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SQUARES OF DEGREES OF BRAUER CHARACTERS AND MONOMIAL BRAUER CHARACTERS Open
Let $G$ be a finite group and let $p$ be a prime factor of $|G|$ . Suppose that $G$ is solvable and $P$ is a Sylow $p$ -subgroup of $G$ . In this note, we prove that $P{\vartriangleleft}G$ and $G/P$ is nilpotent if and only if $\unicode[ST…
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Compact Schur-Weyl duality: Real Lie groups and the cyclotomic Brauer algebra Open
We show that the centraliser of the maximal compact subgroup of the real groups O(p,q) and Sp 2n(R) acting on tensors of their standard representation is isomorphic to the level 2 cyclotomic Brauer algebra with certain parameters in C. We …
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Minimal heights and defect groups with two character degrees Open
Conjecture A of [3] predicts the equality between the smallest positive height of the irreducible characters in a p-block of a finite group and the smallest positive height of the irreducible characters in its defect group. Hence, it can b…
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Universal Triviality of the Chow Group of 0-cycles and the Brauer Group Open
We prove that a smooth proper universally $\textrm{CH}_0$-trivial variety $X$ over a field $k$ has universally trivial Brauer group. This fills a gap in the literature concerning the $p$-torsion of the Brauer group when $k$ has characteris…
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ITÔ’S THEOREM AND MONOMIAL BRAUER CHARACTERS Open
Let $G$ be a finite solvable group and let $p$ be a prime. In this note, we prove that $p$ does not divide $\unicode[STIX]{x1D711}(1)$ for every irreducible monomial $p$ -Brauer character $\unicode[STIX]{x1D711}$ of $G$ if and only if $G$ …
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Cartan matrices and Brauer's $k(B)$-conjecture IV Open
In this note we give applications of recent results coming mostly from the third paper of this series. It is shown that the number of irreducible characters in a $p$-block of a finite group with abelian defect group $D$ is bounded by $|D|$…
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Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties Open
It is well known that the category of quasi-coherent sheaves on a gerbe banded by a diagonalizable group decomposes according to the characters of the group. We establish the corresponding decomposition of the unbounded derived category of…
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Index of fibrations and Brauer classes that never obstruct the Hasse principle Open
Let $X$ be a smooth projective variety with a fibration into varieties that either satisfy a condition on representability of zero-cycles or that are torsors under an abelian variety. We study the classes in the Brauer group that never obs…
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Algebras derived equivalent to Brauer graph algebras and derived invariants of Brauer graph algebras revisited Open
In this paper the class of Brauer graph algebras is proved to be closed under derived equivalence. For that we use the rank of the maximal torus of the identity component of the group of outer automorphisms $Out^0(A)$ of a symmetric stably…
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Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci Open
We describe the Hodge theory of brilliant families of K3 surfaces. Their characteristic feature is a close link between the Hodge structures of any two fibres over points in the Noether-Lefschetz locus. Twistor deformations, the analytic T…
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Gerbes and Brauer groups over stacks Open
The aim of this paper is to develop the theory of Brauer groups for stacks, which are not necessarily algebraic, using gerbes as foundamental tools.
As an application, we focus our attention on Brauer theory for mixed motives: in particu…
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An equivariant bijection between irreducible Brauer characters and weights for Sp(2n, q) Open
The longstanding Alperin weight conjecture and its blockwise version have been reduced to simple groups recently by Navarro, Tiep, Spaeth and Koshitani. Thus, to prove this conjecture, it suffices to verify the corresponding inductive cond…
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Unramified Brauer Group and Its Applications Open
This is a textbook on arithmetic geometry with special regard to unramified Brauer groups of algebraic varieties. The topics include Galois cohomology, Brauer groups, obstructions to stable rationality, arithmetic and geometry of quadrics,…
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Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications Open
In this article we construct three explicit natural subgroups of the Brauer-Picard group of the category of representations of a finite-dimensional Hopf algebra. In examples the Brauer Picard group decomposes into an ordered product of the…
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The blocks with four irreducible characters Open
Suppose that is a Brauer ‐block of a finite group with defect group . If exactly contains four ordinary irreducible characters, then we show that has order four or five, assuming the Alperin–McKay conjecture holds for .
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ITÔ’S THEOREM AND MONOMIAL BRAUER CHARACTERS II Open
Let $G$ be a finite solvable group and let $p$ be a prime. We prove that the intersection of the kernels of irreducible monomial $p$ -Brauer characters of $G$ with degrees divisible by $p$ is $p$ -closed.
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A computational approach to Brauer Witt theorem using Shoda pair theory Open
A classical theorem due to Brauer and Witt implies that every simple component of the rational group algebra QG of a finite group G is Brauer equivalent to a cyclotomic algebra containing Q in its centre. The precise description of this cy…
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On the largest Brauer and p′-character degrees Open
Let K be a field of characteristic p>0. We prove that if all irreducible representations over K of a finite group G have degree at most n, then G has a characteristic subgroup N of index bounded above in terms of n such that its derived su…
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The special Brauer group and twisted Picard varieties Open
We generalise the notion of the Tate-Shafarevich group of an elliptic K3 surface with a section to the Tate-Shafarevich group of a K3 surface endowed with a linear system. The construction, which uses Grothendieck's special Brauer group, p…
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Differential Brauer Monoids Open
The differential Brauer monoid of a differential commutative ring R s defined. Its elements are the isomorphism classes of differential Azumaya R algebras with operation from tensor product subject to the relation that two such algebras ar…
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On Brauer indecomposability of Scott modules Open
Let k be an algebraically closed field of prime characteristic p, G a finite group and P a p-subgroup of G. We investigate the relationship between the fusion system ℱP(G) and the Brauer indecomposability of the Scott kG-module. We give a …