Degree one Milnor K-invariants of groups of multiplicative type

JOURNAL OF ALGEBRA

卷:577

Article

Wertheim, Alexander¹ 

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

关键词: Cohomological invariants;    Algebraic groups;   

DOI  :  10.1016/j.jalgebra.2021.02.020

来源: Elsevier

【 摘 要 】

Let G be a commutative affine algebraic group over a field F, and let H : Fields(F) -> AbGrps be a functor. A (homomorphic) H-invariant of G is a natural transformation Tors(-, G) -> H, where Tors(-, G) is the functor Fields(F) -> AbGrps taking a field extension L/F to the group of isomorphism classes of G(L)-torsors over Spec(L). The goal of this paper is to compute the group Inv(hom)(1) (G, H) of H-invariants of G when G is a group of multiplicative type, and H is the functor taking a field extension L/F to L-x circle times(Z) Q/Z. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free