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Crystalline deformation rings with Hodge--Tate weights between 0 and p

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Speaker: 
Robin Bartlett
Affiliation: 
King's College London/MPIM
Date: 
Wed, 2019-04-10 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

A conjecture of Fontaine--Mazur predicts that many Galois representations arise from geometry. In some cases this conjecture has been proven; an important ingredient in the arguments is an understanding of the geometry of some deformation spaces of Galois representations. I will give an overview of this link, and then will explain an extension of a method, originally due to Kisin, which produces a resolution of these spaces via semi-linear algebra. As a result we can say something about the irreducible components of crystalline deformation rings with Hodge--Tate weights between 0 and p, for unramified extensions of Qp.

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