If one wants to study congruence modulo p among modular forms, a key ingredients is the geometry of the ordinary locus and certain etale covers of it. Hida generalised these ieas to all PEL Shimura varieties with ordinary locus. A generalisation of the ordinary locus is is the mu-ordinary locus, which is never empty. Building on ideas and work of Goldring--Hubert, Pilloni, and Hernandez, we shall explain a general construction of a pro-etale cover of the mu-ordinary locus (the Igusa tower) which can be used to develop Hida theory for all Shimura varieties. The talk will be very introductory and this is joint work (in progress) with Riccardo Brasca.

海报