Separable algebras and coflasque resolutions

Autor:	Ballard, Matthew R., Duncan, Alexander, Lamarche, Alicia, McFaddin, Patrick K.
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory 11E72 (Primary) 12G05 14G25 14G27 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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 precisely when this strategy will fail. Our main result characterizes this invariant in terms of coflasque resolutions of linear algebraic groups introduced by Colliot-Th\'el\`ene. We determine whether or not this invariant is trivial for many fields. For number fields, we show it agrees with the Tate-Shafarevich group of the linear algebraic group, up to behavior at real places. Comment: 31 pages; final version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.06876 Zobrazit plný text záznamu View this record from Arxiv