Extensions of Abelian Schemes and the Additive Group

Fuente: arXiv
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Hauptverfasser: Ribeiro, Gabriel, Rosengarten, Zev
Format: Preprint
Veröffentlicht: 2025
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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