Related papers: Brauer Spaces of Spectral Algebraic Stacks

Using a reduction of the Galois cohomology of a linear algebraic group $G$ to that of a certain finite subquotient, we give different formulas allowing the calculation of the unramified algebraic Brauer group of a homogeneous space…

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…

In this paper we consider the $q$-Brauer algebra over $R$ a commutative noetherian domain. We first construct a new basis for $q$-Brauer algebras, and we then prove that it is a cell basis, and thus these algebras are cellular in the sense…

We investigate a notion of Azumaya algebras in the context of structured ring spectra and give a definition of Brauer groups. We investigate their Galois theoretic properties, and discuss examples of Azumaya algebras arising from Galois…

We investigate the Brauer group of the ring $\mathcal{O}(S)$ of holomorphic functions on a finite-dimensional Stein space S. We provide a purely topological computation of this group and deduce a comparison theorem between the \'etale…

Consider a complete abelian category which has an injective cogenerator. If its derived category is left--complete we show that the dual of this derived category satisfies Brown representability. In particular this is true for the derived…

The classical Skolem--Noether Theorem [Giraud, 71] shows us (1) how we can assign to an Azumaya algebra $A$ on a scheme $X$ a cohomological Brauer class in $H^2(X,\mathbf G_m)$ and (2) how Azumaya algebras correspond to twisted vector…

We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…

An associative central simple algebra is a form of matrices, because a maximal \'{e}tale subalgebra acts on the algebra faithfully by left and right multiplication. In an attempt to extract and isolate the full potential of this point of…

We study the $\mu _N$-gerbe of curves of genus $g$ with an order $N$ automorphism, and explore what corresponding $H^2$-cohomology classes the components of this stack can have. In particular, we look at curves whose quotients by the order…

We show that for complex analytic K3 surfaces any torsion class in H^2(X,O_X^*) comes from an Azumaya algebra. In other words, the Brauer group equals the cohomological Brauer group. For algebraic surfaces, such results go back to…

We use an idea of Rosenberg to prove a reconstruction theorem for abelian categories of alpha-twisted quasi-coherent sheaves on quasi-compact and quasi-separated schemes X when alpha is in the Brauer group of X. By applying the work of…

We study the representation theory of the cyclotomic Brauer algebra via truncation to idempotent subalgebras which are isomorphic to a product of walled and classical Brauer algebras. In particular, we determine the block structure and…

We study families of algebraic varieties parametrized by topological spaces and generalize some classical results such as Hilbert Nullstellensatz and primary decomposition of commutative rings. We show that there is an equivalence between…

We classify absolutely split vector bundles on proper $k$-schemes. More precise, we prove that the closed points of the Picard scheme are in one-to-one correspondence with indecomposable absolutely split vector bundles. Furthermore, we…

Given an algebraic stack $X$, one may compare the derived category of quasi-coherent sheaves on $X$ with the category of dg-modules over the dg-ring of functions on $X$. We study the analogous question in stable homotopy theory, for derived…

We compute the Brauer group of the moduli stack of elliptic curves over the integers, localizations of the integers, finite fields of odd characteristic, and algebraically closed fields of characteristic not $2$. The methods involved…

For algebraic stacks over number fields, we define their Brauer-Manin sets, Brauer-Manin pairings, and extend the descent theory of Colliot-Th\'el\`ene and Sansuc. By extending Sansuc's exact sequence, we show the torsionness of Brauer…

We develop a systematic functional-analytic framework for Hom--Lie Banach algebras, introducing bounded $\alpha$-twisted derivations and almost periodic elements. Under natural continuity and compactness assumptions, we establish a complete…

Let $A$ be a ring equipped with a derivation $\delta $. We study differential Azumaya $A$ algebras, that is, Azumaya $A$ algebras equipped with a derivation that extends $\delta $. We calculate the differential automorphism group of the…