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 over a discretely valued field to contain a unimodular -stable lattice.
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Eva Bayer-Fluckiger, Lenny Taelman, Automorphisms of even unimodular lattices and equivariant Witt groups. J. Eur. Math. Soc. 22 (2020), no. 11, pp. 3467–3490DOI 10.4171/JEMS/991