Automorphisms of even unimodular lattices and equivariant Witt groups

Abstract

We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a 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.