Results 11 to 20 of about 67 (60)

Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties

Documenta Mathematica, 2021
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 complexes of sheaves with quasi-coherent cohomology.
Bergh, Daniel Sven Tobias, Schnürer, Olaf M.   +1 more
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Witt groups of Severi-Brauer varieties and of function fields of conics [PDF]

Épijournal de Géométrie Algébrique
The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a suitable line bundle.
Anne Quéguiner-Mathieu, Jean-Pierre Tignol   +1 more
doaj   +1 more source

Construction of Brauer-Severi Varieties

Contemporary Mathematics, 2021
In this paper, we give an algorithm for computing equations of Brauer-Severi varieties over fields of characteristic 0. As an example, we show the equations of all Brauer-Severi surfaces defined over Q.
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The Picard group of Brauer-Severi varieties

Open Mathematics, 2018
AbstractIn this paper, we provide explicit generators for the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular,we provide such generators for all Brauer-Severi surfaces. To produce these generators we use the theory of twists of smooth plane curves.
Badr, Eslam, Bars, Francesc, Lorenzo García, Elisa   +2 more
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Involutions and Brauer-Severi varieties

Indagationes Mathematicae, 1996
The authors explicitly construct for any finite dimensional central simple algebra \(A\) over a fixed field \(F\) new central simple algebras \(s^2A\) and \(\lambda^2A\), which are Brauer equivalent to the product \(A\otimes A\). With this construction, they then derive, in a characteristic free context, a correspondence between involutions (of the ...
Gatsinzi, J.-B., Tignol, J.-P.
openaire   +2 more sources

More on the Schur group of a commutative ring

International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 2, Page 275-282, 1985., 1985
The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group of R which contain a homomorphic image of a group ring RG for some finite group G. It is the purpose of this article to continue an investigation of this group which was introduced in earlier work as a natural generalization of the Schur group of a field.
R. A. Mollin
wiley   +1 more source

Galois invariants of finite abelian descent and Brauer sets

Bulletin of the London Mathematical Society, Volume 56, Issue 10, Page 3240-3256, October 2024.
Abstract For a variety over a global field, one can consider subsets of the set of adelic points of the variety cut out by finite abelian descent or Brauer–Manin obstructions. Given a Galois extension of the ground field, one can consider similar sets over the extension and take Galois invariants.
Brendan Creutz, Jesse Pajwani, José Felipe Voloch   +2 more
wiley   +1 more source

Arithmetics of homogeneous spaces over p$p$‐adic function fields

Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.
Abstract Let K$K$ be the function field of a smooth projective geometrically integral curve over a finite extension of Qp$\mathbb {Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local–global and weak approximation problems for homogeneous spaces of SLn,K$\textrm {SL}_{n,K}$ with geometric stabilizers ...
Nguyen Manh Linh
wiley   +1 more source

Constructions of Brauer-Severi Varieties and Norm Hypersurfaces

Canadian Journal of Mathematics, 1990
Let k be any field, A a central simple k-algebra of degree m (i.e., dimk A = m2). Several methods of constructing the generic splitting fields for A are proposed and Saltman proves that these methods result in almost the same generic splitting field [8, Theorems 4.2 and 4.4].
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Universal Brauer-Severi varieties

33 pages, some typos corrected, reference to work of Uriya First ...
Gounelas, Frank, Huybrechts, Daniel
openaire   +2 more sources