Results 51 to 60 of about 2,189 (114)
On the Witt group of the punctured spectrum of a regular semilocal ring
Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.Abstract Let R$R$ be a regular semilocal ring of dimension 4q+1⩾5$4q+1\geqslant 5$ which contains 12$\frac{1}{2}$, l⩾1$l\geqslant 1$ the number of maximal ideals of R$R$ which are assumed to be all of the same height, and U$U$ the punctured spectrum of R$R$, that is, SpecR$\operatorname{Spec}R$ without the maximal ideals. We show that the Witt ring W(U)
Stefan Gille, Ivan Panin
wiley +1 more source
The index of projective families of elliptic operators
, 2005 An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X.
Alvarez +13 more
core +2 more sources
Picard sheaves, local Brauer groups, and topological modular forms
Journal of Topology, Volume 17, Issue 2, June 2024.Abstract We develop tools to analyze and compare the Brauer groups of spectra such as periodic complex and real K$K$‐theory and topological modular forms, as well as the derived moduli stack of elliptic curves. In particular, we prove that the Brauer group of TMF$\mathrm{TMF}$ is isomorphic to the Brauer group of the derived moduli stack of elliptic ...
Benjamin Antieau +2 more
wiley +1 more source
The general Ikehata theorem for H‐separable crossed products
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 10, Page 657-662, 2000., 2000 Let B be a ring with 1, C the center of B, G an automorphism group of B of order n for some integer n, CG the set of elements in C fixed under G, Δ = Δ(B, G, f) a crossed product over B where f is a factor set from G × G to U(CG). It is shown that Δ is an H‐separable extension of B and VΔ(B) is a commutative subring of Δ if and only if C is a Galois ...
George Szeto, Lianyong Xue
wiley +1 more source
$K$-Theory of Azumaya algebras
Irish Mathematical Society Bulletin, 2010 For an Azumaya algebra $A$ which is free over its centre $R$, we prove that the $K$-theory of $A$ is isomorphic to $K$-theory of $R$ up to its rank torsion. We observe that a graded central simple algebra, graded by an abelian group, is a graded Azumaya algebra and it is free over its centre.
openaire +2 more sources
The derived category of a non generic cubic fourfold containing a plane
, 2017 We describe an Azumaya algebra on the resolution of singularities of the double cover of a plane ramified along a nodal sextic associated to a non generic cubic fourfold containing a plane.
Moschetti, Riccardo
core +1 more source
Braidings on the category of bimodules, Azumaya algebras and epimorphisms of rings
, 2012 Let $A$ be an algebra over a commutative ring $k$. We prove that braidings on the category of $A$-bimodules are in bijective correspondence to canonical R-matrices, these are elements in $A\ot A\ot A$ satisfying certain axioms. We show that all braidings
Agore, A. L. +2 more
core +1 more source
Centers and Azumaya loci of finite $W$-algebras
, 2020 In this paper, we study the center $Z$ of the finite $W$-algebra $\mathcal{T}(\mathfrak{g},e)$ associated with a semi-simple Lie algebra $\mathfrak{g}$ over an algebraically closed field $\mathds{k}$ of characteristic $p\gg0$, and an arbitrarily given ...
Shu, Bin, Zeng, Yang
core
Twisted derived equivalences for affine schemes [PDF]
, 2013 We show how work of Rickard and To\"en completely resolves the question of when two twisted affine schemes are derived equivalent.Comment: submitted to proceedings; primarily expository; 5 ...
Antieau, Benjamin
core
D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck [PDF]
, 2010 We review first Azumaya geometry and D-branes in the realm of algebraic geometry along the line of Polchinski-Grothendieck Ansatz from our earlier work and then use it as background to introduce Azumaya $C^{\infty}$-manifolds with a fundamental module ...
Liu, Chien-Hao, Yau, Shing-Tung
core