Automorphisms of even unimodular lattices and equivariant Witt groups

2017/08/18 by Bayer-Fluckiger, Eva, Taelman, Lenny · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.05540

Abstract

We characterize the irreducible polynomials that occur as a characteristic polynomial of an automorphism of an even unimodular lattice of given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion in terms of Witt groups for a bilinear form equipped with an action of a group G over a discretely valued field to contain a unimodular G-stable lattice.

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• Non-projective K3 surfaces with real or Salem multiplication
• On Salem numbers of degree 4 and arithmetic hyperbolic orbifolds

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