On the top-dimensional cohomology of arithmetic Chevalley groups

2022/10/23 by Brück, Benjamin, Rego, Yuri Santos, Sroka, Robin J.
#11F75 #20E42 #57M07 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2210.12784

Abstract

Let \mathbbK be a number field with ring of integers \mathfrakO and let G be a Chevalley group scheme not of type \mathttE₈, \mathttF₄ or \mathttG₂. We use the theory of Tits buildings and a result of Tóth on Steinberg modules to prove that H^vcd(G(\mathfrakO); ℚ) = 0 if \mathfrakO is Euclidean.

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