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Title: On the reductions of some crystalline representations
Author: Bartlett, Robin Peter
ISNI:       0000 0004 7660 170X
Awarding Body: King's College London
Current Institution: King's College London (University of London)
Date of Award: 2018
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In this work we study a semilinear category Mod_k^SD which appears as a full subcategory of the category of ρ-torsion Breuil--Kisin modules. We view Mod_k^SD as extending Fontaine-Laffaille theory (for ρ-torsion coefficients) to weights contained in the range [0,p]. As an application we relate the restriction to inertia of a residual representation ρ̄, with the weights ⊂[0,p] for which ρ̄ has a crystalline lift. This allows us to deduce some new cases of the weight part of Serre's conjecture for unitary groups of rank n.
Supervisor: Diamond, Fred Irvin Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available