In this dissertation, we study semi-stable representations of G(Q(p)) and their mod p-reductions, which is a part of the problem in which we construct deformation spaces whose characteristic 0 closed points are the semi-stable lifts with Hodge-Tate weights (0, 1, 2) of a fixed absolutely irreducible residual representation ρ : G(Q(p)) → GL₃(F(p)). We first classify the isomorphism classes of semi-stable representations of G(Q(p)) with regular Hodge-Tate weights, by classifying admissible filtered (phi,N)-modules with Hodge-Tate weights (0, r, s) for 0 < r < s. We also construct a Galois stable lattice in some irreducible semi-stable representations with Hodge-Tate weights (0, 1, 2), by constructing strongly divisible modules, which is an analogue of Galois stable lattices on the filtered (ɸ, N)-module side. We compute the reductions mod p of the corresponding Galois representations to the strongly divisible modules we have constructed, by computing Breuil modules, which is, roughly speaking, mod p-reduction of strongly divisible modules. We also determine which Breuil modules corresponds to irreducible mod p representations of G(Q(p)).
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/293444 |
| Date | January 2013 |
| Creators | Park, Chol |
| Contributors | Savitt, David, Cais, Bryden, Sharifi, Romyar, Thakur, Dinesh, Savitt, David |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Electronic Dissertation |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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