Joint IAS/Princeton University Number Theory Seminar

Local-global compatibility in the crystalline case

Let F be a CM field. Scholze constructed Galois representations associated to classes in the cohomology of locally symmetric spaces for GL_n/F with p-torsion coefficients. These Galois representations are expected to satisfy local-global compatibility at primes above p. Even the precise formulation of this property is subtle in general, and uses Kisin’s potentially semistable deformation rings. However, this property is crucial for proving modularity lifting theorems. I will discuss joint work with J. Newton, where we establish local-global compatibility in the crystalline case under mild technical assumptions. This relies on a new idea of using P-ordinary parts, and improves on earlier results obtained in joint work with P. Allen, F. Calegari, T. Gee, D. Helm, B. Le Hung, J. Newton, P. Scholze, R. Taylor, and J. Thorne in certain Fontaine-Laffaille cases.

Date & Time

April 16, 2020 | 3:00pm – 4:00pm

Location

https://theias.zoom.us/j/959183254

Affiliation

Imperial College

Event Series

Categories

Notes

Please note that this seminar will take place online via Zoom. You can connect to this seminar via the following link and password: https://theias.zoom.us/j/959183254 Password: the three digit integer that is the cube of the sum of its digits