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Title: The Breuil-Mézard conjecture when l is not equal to p
Author: Shotton, Jack
ISNI:       0000 0004 7233 0359
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2015
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Let l and p be primes, let F/Q_p be a finite extension with absolute Galois group G_F, let F be a finite field of characteristic l, and let p̄ : G_F→ GL_n(F) be a continuous representation. Let R^□(p̄) be the universal framed deformation ring for p̄. If l = p, then the Breuil-Mézard conjecture relates the mod l reduction of certain cycles in R^□(p̄) to the mod l reduction of certain representations of GL_n(O_F). We give an analogue of the Breuil-Mézard conjecture when l ≠ p, and prove it whenever l > 2 using automorphy lifting theorems. We also give a local proof when n = 2 and l> 2 by explicit calculation, and also when l is "quasi-banal'' for F and p̄ is tamely ramified.
Supervisor: Gee, Toby Sponsor: Engineering and Physical Sciences Research Council ; Leverhulme Trust
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral