In this seminar, we introduce Bruhat-Tits theory of p-adic reductive groups, then we study the type theory established by J.-K. Yu, J.-L. Kim, J. Fintzen. Finally, we will see recent applications on l-modular representations of p-adic groups.

References:

1. Kaletha T, Prasad G. Bruhat–Tits Theory: A New Approach. Cambridge University Press; 2023.

2. Ju-Lee Kim, Supercuspidal representations: an exhaustion theorem, J. Amer. Math. Soc. 20 (2007), no. 2, 273–320 (electronic).

3. Jiu-Kang Yu, Construction of tame supercuspidal representations, J. Amer. Math. Soc. 14 (2001), no. 3, 579–622 (electronic).

4. Types for tame p-adic groups. Annals of Mathematics 193 no. 1 (2021), pp. 303-346.

5. Parametrization and reduction to depth zero of Z[1/p]-blocks of tame p-adic groups. With Jean-François Dat.