Functorial splitting of l-adic cohomology in exact sequences of group varieties

2023/12/06 by de Vries, Victor
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.03501

Abstract

In this document we consider an exact sequence of group varieties e→ N→ G→ Q→ e over an algebraically closed field. We show that for l≠ char(k) a prime there exists an isomorphism of graded ℚ_l-algebras H_ét^*(G,ℚ_l)≅ H_ét^*(N,ℚ_l)⊗_ℚlH_ét^*(Q,ℚ_l) that is compatible with pullback homomorphisms f^* of endomorphisms f:G→ G that stabilize N.

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