# On deformations of $1$-motives

## TL;DR

This paper extends the classical Serre-Tate deformation equivalence from abelian varieties to 1-motives, broadening the understanding of deformation theory in algebraic geometry.

## Contribution

It generalizes the Serre-Tate theorem to include 1-motives, providing new insights into their deformation theory in positive characteristic.

## Key findings

- Deformation theory of 1-motives parallels that of Barsotti-Tate groups.
- Extension of Serre-Tate theorem to 1-motives.
- Enhanced understanding of infinitesimal deformations in algebraic geometry.

## 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.