G-valued flat deformations and local models

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• Brandon Levin (IAS, Princeton)
• Tuesday 26 November 2013, 16:15-17:15
• MR13.

If you have a question about this talk, please contact James Newton.

I will begin with a brief introduction to the deformation theory of Galois representations and its role in modularity lifting. This will motivate the study of local deformation rings and more specifically flat deformation rings. I will then discuss Kisin’s resolution of the flat deformation ring at l = p and describe conceptually the importance of local models of Shimura varieties in analyzing its geometry. Finally, I will address how to generalize these results from GL_n to a general reductive group G. If time permits, I will describe briefly the role that recent advances in p-adic Hodge theory and local models of Shimura varieties play in this situation.

This talk is part of the Number Theory Seminar series.

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