English

Characteristic polynomials of isometries of even unimodular lattices

Number Theory 2024-01-24 v1 Algebraic Geometry

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 1010 or 1818 to be realized as the dynamical degree of an automorphism of nonprojective K3 surface, in terms of its minimal polynomial.

Keywords

Cite

@article{arxiv.2401.12620,
  title  = {Characteristic polynomials of isometries of even unimodular lattices},
  author = {Yuta Takada},
  journal= {arXiv preprint arXiv:2401.12620},
  year   = {2024}
}