2020
DOI: 10.48550/arxiv.2006.06876
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Separable algebras and coflasque resolutions

Abstract: Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects. The most famous example is the deep connection between Severi-Brauer varieties and central simple algebras. For more general varieties, one might use endomorphism algebras of line bundles, of indecomposable vector bundles, or of exceptional objects in their derived categories.Using Galois cohomology, we describe a new invariant of reductive algebraic groups that captures prec… Show more

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Cited by 1 publication
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“…Torsors invisible to Brauer invariants. We recall the set Ж(k, G) introduced in [BDLM20]. A separable algebra over k is a finite direct sum of matrix algebras over finite dimensional division rings whose centers are finite separable field extensions of k. Let G be a connected reductive algebraic group over k; for example, a torus.…”
Section: 2mentioning
confidence: 99%
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“…Torsors invisible to Brauer invariants. We recall the set Ж(k, G) introduced in [BDLM20]. A separable algebra over k is a finite direct sum of matrix algebras over finite dimensional division rings whose centers are finite separable field extensions of k. Let G be a connected reductive algebraic group over k; for example, a torus.…”
Section: 2mentioning
confidence: 99%
“…Proof. This is stated in the introduction of [BDLM20]. It follows from [BDLM20, Theorem 2] since, Ж(k v , T v ) = * for any real place v. Indeed, any k v -torus is rational and Ж is a birational invariant of tori [BDLM20, Proposition 4.2].…”
Section: 2mentioning
confidence: 99%