Ranks of 1-motives as dimensions of Ext$^1$ vector spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915039786565632 |
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| author | Nesa, Nicola |
| author_facet | Nesa, Nicola |
| contents | We reformulate the ranks that appear in the dimension formula for the linear space of periods of a 1-motive established by Huber and Wüstholz in a more conceptual and categorical way, as dimensions of Ext$^1$ vector spaces. This constitutes the first step towards rewriting the dimension formula purely in general categorical terms, rather than through definitions and computations introduced ad hoc for 1-motives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04271 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ranks of 1-motives as dimensions of Ext$^1$ vector spaces Nesa, Nicola Number Theory Algebraic Geometry 11J72, 11J86, 14C15, 18E10 We reformulate the ranks that appear in the dimension formula for the linear space of periods of a 1-motive established by Huber and Wüstholz in a more conceptual and categorical way, as dimensions of Ext$^1$ vector spaces. This constitutes the first step towards rewriting the dimension formula purely in general categorical terms, rather than through definitions and computations introduced ad hoc for 1-motives. |
| title | Ranks of 1-motives as dimensions of Ext$^1$ vector spaces |
| topic | Number Theory Algebraic Geometry 11J72, 11J86, 14C15, 18E10 |
| url | https://arxiv.org/abs/2403.04271 |