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arXiv · 2401.12620

Characteristic polynomials of isometries of even unimodular lattices

Yuta Takada
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Abstract

E. Bayer-Fluckiger gave a necessary and sufficient condition for a polynomial to be realized as the characteristic polynomial of a semisimple isometry of an even unimodular lattice, by describing the local-global obstruction, and the author extended the result. This article presents a systematic way to compute the obstruction. As an application, we give a necessary and sufficient condition for a Salem number of degree $10$ or $18$ to be realized as the dynamical degree of an automorphism of nonprojective K3 surface, in terms of its minimal polynomial.

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Yuta Takada. 2024-01-23. Characteristic polynomials of isometries of even unimodular lattices. https://arxiv.org/abs/2401.12620

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