On the slope filtration of [phi]-modules over the Robba ring
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2009
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| Online Access: | http://hdl.handle.net/1721.1/45350 |
| _version_ | 1826206013689167872 |
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| author | Liu, Ruochuan |
| author2 | Kiran Sridhara Kedlaya. |
| author_facet | Kiran Sridhara Kedlaya. Liu, Ruochuan |
| author_sort | Liu, Ruochuan |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. |
| first_indexed | 2024-09-23T13:22:37Z |
| format | Thesis |
| id | mit-1721.1/45350 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:22:37Z |
| publishDate | 2009 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/453502019-04-12T09:56:58Z On the slope filtration of [phi]-modules over the Robba ring Liu, Ruochuan Kiran Sridhara Kedlaya. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2009-04-29T17:29:12Z 2009-04-29T17:29:12Z 2008 2008 Thesis http://hdl.handle.net/1721.1/45350 316801430 eng 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. http://dspace.mit.edu/handle/1721.1/7582 65 leaves application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Liu, Ruochuan On the slope filtration of [phi]-modules over the Robba ring |
| title | On the slope filtration of [phi]-modules over the Robba ring |
| title_full | On the slope filtration of [phi]-modules over the Robba ring |
| title_fullStr | On the slope filtration of [phi]-modules over the Robba ring |
| title_full_unstemmed | On the slope filtration of [phi]-modules over the Robba ring |
| title_short | On the slope filtration of [phi]-modules over the Robba ring |
| title_sort | on the slope filtration of phi modules over the robba ring |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/45350 |
| work_keys_str_mv | AT liuruochuan ontheslopefiltrationofphimodulesovertherobbaring |