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# On deformations of $1$-motives

Published:2018-03-22

• A. Bertapelle,
Dipartimento di Matematica "Tullio Levi-Civita", Università degli Studi di Padova , via Trieste, 63 , I-35121 Padova, Italy
• N. Mazzari,
Institut de Mathématiques de Bordeaux, University of Bordeaux, F-33405 Talence cedex, France
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## Abstract

According to a well-known theorem of Serre and Tate, the infinitesimal deformation theory of an abelian variety in positive characteristic is equivalent to the infinitesimal deformation theory of its Barsotti-Tate group. We extend this result to $1$-motives.
 Keywords: $1$-motive, Barsotti-Tate group
 MSC Classifications: 14L15 - Group schemes 14C15 - (Equivariant) Chow groups and rings; motives 14L05 - Formal groups, $p$-divisible groups [See also 55N22]

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