Relative p-adic Hodge theory and Rapoport- Zink period domains
نویسنده
چکیده
As an example of relative p-adic Hodge theory, we sketch the construction of the universal admissible filtration of an isocrystal (φ-module) over the completion of the maximal unramified extension of Qp, together with the associated universal crystalline local system. Mathematics Subject Classification (2000). Primary 14G22; Secondary 11G25.
منابع مشابه
Slope filtrations and (φ,Γ)-modules in families
These are the notes for a three-lecture minicourse given at the Institut Henri Poincaré in January 2010 as part of the Galois Trimester. The first lecture reviews the theory of slopes and slope filtrations for Frobenius actions (φ-modules) over the Robba ring, the link to p-adic Hodge theory via the work of Berger, and the analogue of Dieudonné-Manin classifications over the Robba ring. The sec...
متن کاملTowards a theory of local Shimura varieties
This is a survey article that advertises the idea that there should exist a theory of p-adic local analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces defined by Rapoport–Zink spaces, and we also review their theory in the light of this idea. We also discuss conjectures on the l-adic cohomology of local Shimura varieties.
متن کاملWEIGHT-MONODROMY CONJECTURE FOR p-ADICALLY UNIFORMIZED VARIETIES
The aim of this paper is to prove the weight-monodromy conjecture (Deligne’s conjecture on the purity of monodromy filtration) for varieties with p-adic uniformization by the Drinfeld upper half spaces of any dimension. The ingredients of the proof are to prove a special case of the Hodge standard conjecture, and apply an argument of Steenbrink, M. Saito to the weight spectral sequence of Rapop...
متن کاملPolarization Measurement aboard the Satellite and Solution of the Emission Mechanism of the Gamma-Ray Bursts
Tetsushi Ito (Kyoto University, Graduate School of Science, Assistant Professor) 【Outline of survey】 Shimura varieties are algebraic varieties (geometric objects defined by equations), which are generalizations of modular curves. Previously, several mathematical objects in arithmetic geometry, Galois representations, automorphic representations were studied from individual perspectives. However...
متن کاملWeight-monodromy Conjecture for Certain Threefolds in Mixed Characteristic
The weight-monodromy conjecture claims the coincidence of the shifted weight filtration and the monodromy filtration on étale cohomology of a proper smooth variety over a complete discrete valuation field. Although it was already proved in some cases, the case of dimension ≥ 3 in mixed characteristic is still unproved up to now. The aim of this paper is to prove the weight-monodromy conjecture ...
متن کامل