Abstract:

This lecture series aims to give an introduction to some recent progress on the mod p Langlands program for GL_2. It will cover the following topics:

(i) Serre weights and Breuil-Paskunas’ construction;
(ii) Gelfand-Kirillov dimension of some representations of GL2;
(iii) Finite length results;
(iv) Generalized Colmez’s functor.

Reference:

1. C. Breuil, F. Herzig, Y. Hu, S. Morra, B. Schraen, Gelfand-Kirillov dimension and mod p cohomology for GL2, arXiv:2009.03127
2. C. Breuil, F. Herzig, Y. Hu, S. Morra, B. Schraen, Conjectures and results on mod p representations of GLn for a p-adic field K, arXiv:2102.06188
3. C. Breuil, V. Paskunas, Towards a mod p Langlands correspondence for GL2, Memoirs of AMS 216 (2012).
4. M. Emerton, T. Gee, D. Savitt,  Lattices in the cohomology of Shimura curves, Invent. Math. 200 (2015).
5. Y. Hu, H. Wang, On the mod p cohomology for GL2: the non-semisimple case, Cambridge J. Math 10 (2022).

Time:

11/2、11/9、11/16、11/23    10:00-12:00