Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Monday, 2 February 2009, 11:00–12:00, Sn403

Urs Hartl: The equal characteristic analog of Fontaine-Theory

Abstract:

We construct period spaces for Hodge structures in equal characteristic. These Hodge structures were invented by Pink. The period spaces are analogues of the Rapoport-Zink period spaces for Fontaine's filtered isocrystals in mixed characteristic. For our period spaces we prove the analogue of a conjecture of Rapoport-Zink stating the existence of interesting local systems on a Berkovich open subspace of the period space. Moreover, we prove the analogue of the Colmez-Fontaine Theorem that "weakly admissible implies admissible". As a consequence the Berkovich open subspace mentioned above contains every classical rigid analytic point of the period space.