2026-09-19T23:13:41Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/453502022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Kiran Sridhara Kedlaya.
Liu, Ruochuan
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2009-04-29T17:29:12Z
2009-04-29T17:29:12Z
2008
2008
http://hdl.handle.net/1721.1/45350
316801430
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).
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.
by Ruochuan Liu.
Ph.D.
65 leaves
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
On the slope filtration of [phi]-modules over the Robba ring
Thesis
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<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.</Abstract>
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