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We characterize the irreducible polynomials that occur as a characteristicpolynomial 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 ageneral criterion in terms of Witt groups for a bilinear form equipped with anaction of a group G over a discretely valued field to contain a unimodularG-stable lattice.

Automorphisms of even unimodular lattices and equivariant Witt groups