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Breuil-Mézard conjectures for central division algebras

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Title: Breuil-Mézard conjectures for central division algebras
Authors: Dotto, Andrea
Item Type: Thesis or dissertation
Abstract: We give a parametrization of the inertial classes of smooth representations of inner forms of GL(n) over a p-adic field, based on type-theoretic invariants. Then we give a complete description of the behaviour of this parametrization under the Jacquet–Langlands correspondence, proving a conjecture of Broussous, Sécherre and Stevens on preservation of endo-classes. As an application of this result, we construct a Jacquet–Langlands transfer of types and Serre weights for central division algebras, and use it to deduce a form of the Breuil–Mézard conjecture, for discrete series Galois deformation rings and types of central division algebras, from the conjectural statement for GL(n).
Content Version: Open Access
Issue Date: Jul-2019
Date Awarded: Aug-2019
URI: http://hdl.handle.net/10044/1/81636
DOI: https://doi.org/10.25560/81636
Copyright Statement: Creative Commons Attribution NonCommercial NoDerivatives Licence
Supervisor: Gee, Toby
Buzzard, Kevin
Sponsor/Funder: Engineering and Physical Sciences Research Council
Funder's Grant Number: EP/L015234/1
Department: Mathematics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Mathematics PhD theses



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