I will first recall Grothendieck's notion of n-truncated Barsotti-Tate group. Such groups form an algebraic stack over the integers. The problem is to give an illuminating description of its reductions modulo powers of p. A related problem is to construct analogs of these reductions related to general Shimura varieties with good reduction at p. Some time ago I formulated conjectures which address these problems. The conjectures have been proved by Z.Gardner, K.Madapusi, and A.Mathew. In particular, they developed a modern version of Dieudonné theory.
By Jorgen Ellegaard Andersen
By Alexander Goncharov
By Mina Aganagic
By Yan Soibelman
By Tony Pantev
By Kenji Fukaya
By Denis Auroux
By Davide Gaiotto
By Yuri Tschinkel
By Pavel Etingof
By Alexander Odesskii
