On the slope filtration of [phi]-modules over the Robba ring

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated étale ([phi], [Gamma])-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily étale (([phi], [Gamma])-modules over the Robba ring, of the Euler-Poincaré characteristic formula and Tate local duality for p-adic representations. These results are expected to intervene in the duality theory for Selmer groups associated to de Rham representations. We introduce the notion of families of [phi]-modules which arises naturally from both rigid cohomology and p-adic Hodge theory. We then prove the local constancy of generic HN-polygons of families of overconvergent [phi]-modules and the semicontinuity of HN-polygons of families of [phi]-modules over reduced affinoid algebras. These results are prospective for a slope theory of families of (overconvergent) [phi]-modules.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Liu, Ruochuan

Advisor dc:contributor.advisor

• Kiran Sridhara Kedlaya.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/45350

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/45350