A comparison theorem for ordinary p-adic modular forms

Abstract: I will discuss joint work in progress with Elena Mantovan and James Newton, whose goal is to compare ordinary completed cohomology with (higher) Hida theory, in the special case of the modular curve. Both these notions go back to Hida, though the former can be reinterpreted using Emerton’s functor of ordinary parts applied to completed cohomology, and the latter has been redeveloped and expanded recently by Boxer and Pilloni to incorporate higher coherent cohomology. Our work gives a new proof to a theorem of Ohta, that is perhaps more amenable to generalisation. The key ingredients are the Bruhat stratification on the Hodge-Tate period domain, and the integral comparison results pioneered by Bhatt, Morrow and Scholze.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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