Related papers: The period-index problem for complex tori

We study the geometry of the (generalized) twistor triangles $\triangle J_1J_2J_3$ in the period domain of compact complex tori of complex dimension $2n$ by the means of the representation theory of the algebras (of real dimension 8)…

We prove that every Brauer class over a field splits over a torsor under an abelian variety. If the index of the class is not congruent to 2 modulo 4, we show that the Albanese variety of any smooth curve of positive genus that splits the…

In this paper we describe all indecomposable two-term partial tilting complexes over a Brauer tree algebra with multiplicity 1 using a criterion for a minimal projective presentation of a module to be a partial tilting complex. As an…

We use the Serre-Godeaux varieties of finite groups, projective representation theory, the twisted Atiyah-Segal completion theorem, and our previous work on the topological period-index problem to compute the etale index of Brauer classes…

Answering a question of P\'alfy and Pyber, we first prove the following extension of the k(GV)-Problem: Let G be a finite group and A\le Aut(G) such that (|G|,|A|)=1. Then the number of conjugacy classes of the semidirect product GA is at…

For a homogeneous space X of a connected algebraic group G (with connected stabilizers) over a field k of characteristic zero, we construct a canonical complex of Galois modules of length 3 and a canonical isomorphism between an…

In this paper we prove an analogue of Brauer's theorem for faithful objects in fusion categories. Other notions, such as the order and the index associated to faithful objects of fusion categories are also discussed. We show that the index…

We study 2-term tilting complexes of Brauer tree algebras in terms of simplicial complexes. We show the symmetry and convexity of the simplicial complexes as lattice polytopes. Via a geometric interpretation of derived equivalences, we show…

Let $L$ be a number field and let $E/L$ be an elliptic curve with complex multiplication by the ring of integers $\mathcal{O}_K$ of an imaginary quadratic field $K$. We use class field theory and results of Skorobogatov and Zarhin to…

We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over the field of complex numbers this is an elementary abelian 2-group with an explicit upper…

The notion of index for arbitrary real factors is introduced and investigated. The main tool in our approach is the reduction of real factors to involutive *-anti-automorphisms of their complex enveloping von Neumann algebras. Similar to…

Problem 21 of Brauer's list of problems from 1963 asks whether for any positive integer k there are finitely many isomorphism classes of groups that occur as the defect group of a block with k irreducible characters. We solve this problem…

In this paper we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a riemannian \'etale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for…

We give an algorithm to explicitly determine all elements of the $q$-torsion (for $q$ an odd prime) of the Brauer group of an elliptic curve over any base field of characteristic different from $q$, containing a primitive $q$-th root of…

We consider a Kepler problem in dimension two or three, with a time-dependent $T$-periodic perturbation. We prove that for any prescribed positive integer $N$, there exist at least $N$ periodic solutions (with period $T$) as long as the…

We prove the existence of Ulrich bundles on any Brauer--Severi variety. In some cases, the minimal possible rank of the obtained Ulrich bundles equals the period of the Brauer--Severi variety. Moreover, we find a formula for the rank of an…

We give a closed formula for recovering a non-hyperelliptic genus three curve from its period matrix, and derive some identities between Jacobian Nullwerte in dimension three.

Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph…

Let $X$ be a smooth projective curve over the complex numbers. We compute the Brauer group of the moduli stack of Bruhat-Tits group scheme $\mathcal{G}$-torsors on $X$. When $g(X) \geq 3$ we compute the Brauer group of the regularly stable…

The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional $\sk$-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of…