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arXiv · 2506.17393

Extensions of Abelian Schemes and the Additive Group

Gabriel Ribeiro·Zev Rosengarten
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Abstract

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.

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Gabriel Ribeiro, Zev Rosengarten. 2025-06-20. Extensions of Abelian Schemes and the Additive Group. https://arxiv.org/abs/2506.17393

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