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.
$1$-motive, Barsotti-Tate group
14L15 - Group schemes
14C15 - (Equivariant) Chow groups and rings; motives
14L05 - Formal groups, $p$-divisible groups [See also 55N22]