Chai's conjectures on base change conductors
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917440805404672 |
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| author | Overkamp, Otto Suzuki, Takashi |
| author_facet | Overkamp, Otto Suzuki, Takashi |
| contents | The base change conductor is an invariant introduced by Chai which measures the failure of a semiabelian variety to have semiabelian reduction. We investigate the behaviour of this invariant in short exact sequences, as well as under duality and isogeny. Our results imply Chai's conjecture on the additivity of the base change conductor in short exact sequences, while also showing that a proposed generalisation of this conjecture fails. We use similar methods to show that the base change conductor is invariant under duality of Abelian varieties in equal positive characteristic (answering a question of Chai), as well as giving a new short proof of a formula due to Chai, Yu, and de Shalit which expresses the base change conductor of a torus in terms of its (rational) cocharacter module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01289 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Chai's conjectures on base change conductors Overkamp, Otto Suzuki, Takashi Number Theory Algebraic Geometry 14K15 (Primary), 14G20, 11G45, 14F20, 11G10 (Secondary) The base change conductor is an invariant introduced by Chai which measures the failure of a semiabelian variety to have semiabelian reduction. We investigate the behaviour of this invariant in short exact sequences, as well as under duality and isogeny. Our results imply Chai's conjecture on the additivity of the base change conductor in short exact sequences, while also showing that a proposed generalisation of this conjecture fails. We use similar methods to show that the base change conductor is invariant under duality of Abelian varieties in equal positive characteristic (answering a question of Chai), as well as giving a new short proof of a formula due to Chai, Yu, and de Shalit which expresses the base change conductor of a torus in terms of its (rational) cocharacter module. |
| title | Chai's conjectures on base change conductors |
| topic | Number Theory Algebraic Geometry 14K15 (Primary), 14G20, 11G45, 14F20, 11G10 (Secondary) |
| url | https://arxiv.org/abs/2310.01289 |