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dc.contributor.advisorKiran Sridhara Kedlaya.en_US
dc.contributor.authorLiu, Ruochuanen_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2009-04-29T17:29:12Z
dc.date.available2009-04-29T17:29:12Z
dc.date.copyright2008en_US
dc.date.issued2008en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/45350
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.en_US
dc.descriptionIn title on title page, [phi] appears as lower case Greek letter.en_US
dc.descriptionIncludes bibliographical references (leaves 63-65).en_US
dc.description.abstractGiven 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.en_US
dc.description.statementofresponsibilityby Ruochuan Liu.en_US
dc.format.extent65 leavesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleOn the slope filtration of [phi]-modules over the Robba ringen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.identifier.oclc316801430en_US


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