Characteristic polynomials of isometries of even unimodular lattices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914649152159744 |
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| author | Takada, Yuta |
| author_facet | Takada, Yuta |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_12620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characteristic polynomials of isometries of even unimodular lattices Takada, Yuta Number Theory Algebraic Geometry 11H56, 14J28 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. |
| title | Characteristic polynomials of isometries of even unimodular lattices |
| topic | Number Theory Algebraic Geometry 11H56, 14J28 |
| url | https://arxiv.org/abs/2401.12620 |