6 avril 2021

James Newton (King's College de Londres)
Comparison theorems for ordinary p-adic modular forms

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Lieu : Séminaire en ligne

Résumé : I will discuss work in progress with Ana Caraiani and Elena Mantovan, the goal of which is to compare ordinary completed cohomology of Shimura varieties with coherent cohomology groups appearing in (higher) Hida theory. I will focus on the special case of the modular curve, where our results give a new proof of a theorem of Ohta and there are also related results of Rodriguez Camargo in the finite slope context.
The two incarnations of p-adic modular forms we are comparing go back to Hida, although the former can be reinterpreted using Emerton’s functor of ordinary parts, and the latter has been expanded recently by Boxer and Pilloni to incorporate higher coherent cohomology. The key ingredients in our work are the Bruhat stratification on the Hodge-Tate period domain, and some part of the integral p-adic Hodge theory of Bhatt, Morrow and Scholze.

Comparison theorems for ordinary p-adic modular forms  Version PDF