Essential dimension of cohomology classes via valuation theory

2024/01/16 by Ofek, Danny, Reichstein, Zinovy · 1 citation
#12G05 #12J20 #16K50 #19C30 #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2401.08532

Abstract

We give a formula for the essential dimension of a cohomology class α in H^d(K, ℚ_p/ℤ_p (d)) when K is a strictly Henselian field. This formula is particularly explicit in the case, where α is a Brauer class (for d = 2). As an application of our bound with d = 3, we study the essential dimension of exceptional groups by examining the image of the Rost invariant.

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