On the slope filtration of [phi]-modules over the Robba ring
Name
316801430-MIT.pdf
Description
Full printable version
Size
2.97 MB
Format
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Checksum (MD5)
b93f00c6ef07ca90c0ae28238a7c2087
Author(s)
Liu, Ruochuan
Advisor(s)
Kiran Sridhara Kedlaya.
Date Issued
2008
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
In title on title page, [phi] appears as lower case Greek letter.
Includes bibliographical references (leaves 63-65).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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