On the \mathbbA¹-Euler characteristic of the variety of maximal tori in a reductive group

2020/11/30 by Ananyevskiy, Alexey
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.14613

Abstract

We show that for a reductive group G over a field k the \mathbbA¹-Euler characteristic of the variety of maximal tori in G is an invertible element of the Grothendieck-Witt ring GW(k), settling the weak form of a conjecture by Fabien Morel. As an application we obtain a generalized splitting principle which allows one to reduce the structure group of a Nisnevich locally trivial G-torsor to the normalizer of a maximal torus.

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