Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911205690441728 |
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| author | Lin, Alice |
| author_facet | Lin, Alice |
| contents | Using integral $p$-adic Hodge theory, Kato and Koshikawa define a generalization of the Faltings height of an abelian variety to motives defined over a number field. Assuming the adelic Mumford-Tate conjecture, we prove a finiteness property for heights in the isogeny class of a motive, where the isogenous motives are not required to be defined over the same number field. This expands on a result of Kisin and Mocz for the Faltings height in isogeny classes of abelian varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction Lin, Alice Number Theory Algebraic Geometry Using integral $p$-adic Hodge theory, Kato and Koshikawa define a generalization of the Faltings height of an abelian variety to motives defined over a number field. Assuming the adelic Mumford-Tate conjecture, we prove a finiteness property for heights in the isogeny class of a motive, where the isogenous motives are not required to be defined over the same number field. This expands on a result of Kisin and Mocz for the Faltings height in isogeny classes of abelian varieties. |
| title | Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2510.10403 |