Serre–Tate theorem

In algebraic geometry, the Serre–Tate theorem, Serre and Tate (1964) says that an abelian scheme and its p-divisible group have the same infinitesimal deformation theory. This was first proved by Serre when the reduction of the abelian variety is ordinary, using the Greenberg functor; then Tate gave a proof in the general case by a different method. Their proofs were not published, but they were summarized in the notes of the Lubin-Serre-Tate seminar (Woods Hole, 1964). Other proofs were published by Messing (1962) and Drinfeld (1976).