Extensions of Abelian Schemes and the Additive Group
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912443125465088 |
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| author | Ribeiro, Gabriel Rosengarten, Zev |
| author_facet | Ribeiro, Gabriel Rosengarten, Zev |
| contents | We compute extension sheaves of abelian schemes and of the additive group by the multiplicative group in the fppf topology. Our main results include a generalized and streamlined proof of the Barsotti--Weil formula, the vanishing of $\underline{\operatorname{Ext}}^2(A,\mathbb{G}_m)$ for an abelian scheme $A$ over a general base, and a description of $\underline{\operatorname{Ext}}^1(\mathbb{G}_a,\mathbb{G}_m)$ in characteristic zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions of Abelian Schemes and the Additive Group Ribeiro, Gabriel Rosengarten, Zev Algebraic Geometry Number Theory We compute extension sheaves of abelian schemes and of the additive group by the multiplicative group in the fppf topology. Our main results include a generalized and streamlined proof of the Barsotti--Weil formula, the vanishing of $\underline{\operatorname{Ext}}^2(A,\mathbb{G}_m)$ for an abelian scheme $A$ over a general base, and a description of $\underline{\operatorname{Ext}}^1(\mathbb{G}_a,\mathbb{G}_m)$ in characteristic zero. |
| title | Extensions of Abelian Schemes and the Additive Group |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2506.17393 |