Date and time: 11 Jan, 2021, 13:00-14:00











Speaker:  Francesco Maria Saettone















Title:  Gross' Canonical and Quasi-canonical Liftings

Abstract: The goal of this talk is to give an account on Gross' seminal paper on canonical and quasi-canonical liftings of formal modules.
Except for basic notions on formal groups, this talk is intended to be self-contained. 

The first main result we will consider is an explicit description of the ring of endomorphism of some reduction of the canonical lifting, and to do this we will briefly introduce the notion of formal cohomology introduced by Lubin and Tate. Secondly, it will be proven that quasi-canonical liftings are isogenous to the canonical lifting, and the set of isomorphism classes of quasi-canonical liftings together with its Galois action will be determined.

These ideas are deeply related with the deformations of formal groups (equivalently of connected p-divisible groups) and several relatively recent applications to arithmetic have been discovered, for instance in the proofs of some Arithmetic Fundamental Lemmas. 









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https://huji.zoom.us/j/85259021329?pwd=RndGa0VNRjFMQ3hXYkJRb1k5ZGFkQT09

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Recordings can be found here: http://math.huji.ac.il/~shnidman/Lunchseminars.html