| Résume | Fix a $p$-divisible group over an algebraically closed field of characteristic $p$ and consider its deformations to characteristic zero. In 1970 Grothendieck posed the question to determine the set of all Hodge filtrations which can occur as the Hodge filtration of such a deformation. It is a subset of a Grassmannian. As a first step Rapoport and Zink constructed in their book a rigid-analytic period space $F_{wa}$ inside this Grassmannian which contains all these Hodge filtrations. In my talk I show that however, almost always $F_{wa}$ contains Berkovich points which do not correspond to Hodge filtrations, and I construct a Berkovich open subspace $F_a$ of $F_{wa}$ which I conjecture to be the answer to Grothendieck's question. (Preprint on arXiv:math.NT/0605254 ) |
