Results 1 to 10 of about 59 (52)
The Picard group of Brauer-Severi varieties
Open Mathematics, 2018 In 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.
Badr Eslam +2 more
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On the section conjecture and Brauer–Severi varieties [PDF]
Mathematische Zeitschrift, 2021 AbstractJ. Stix proved that a curve of positive genus over $$\mathbb {Q}$$ Q which maps to a non-trivial Brauer–Severi variety satisfies the section conjecture. We prove that, if X is a curve of positive genus over a number field k and the Weil restriction $$R_{k/\mathbb {Q}}X$$
exaly +7 more sources
Genus one curves and Brauer–Severi varieties [PDF]
Mathematical Research Letters, 2012 comments ...
Wei Ho
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Absolutely split locally free sheaves on proper k-schemes and Brauer–Severi varieties
Bulletin Des Sciences MathematiquesWe 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 apply the obtained results to study the geometry of (generalized) Brauer--Severi varieties.
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Ulrich bundles on Brauer–Severi varieties [PDF]
Proceedings of the American Mathematical Society, 2023 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 Ulrich bundle involving the period of the considered Brauer–Severi variety
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The index of a Brauer class on a Brauer-Severi variety [PDF]
Transactions of the American Mathematical Society, 1992 Let D D and E
Schofield, Aidan, Van den Bergh, Michel
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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 +1 more
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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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Witt groups of Severi-Brauer varieties and of function fields of conics [PDF]
Épijournal de Géométrie AlgébriqueThe 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 +1 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.
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