Lower bounds on the essential dimension of reductive groups

2024/11/06 by Ofek, Danny
#11E72 #12G05 #12J20 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2411.03789

Abstract

We introduce a technique for proving lower bounds on the essential dimension of split reductive groups. As an application, we strengthen the best previously known lower bounds for various split simple algebraic groups, most notably for the exceptional group E₈. In the case of the projective linear group PGL_n, we recover A. Merkurjev's celebrated lower bound with a simplified proof. Our technique relies on decompositions of loop torsors over valued fields due to P. Gille and A. Pianzola.

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