Shankar Project

More details on the project will be provided here as they become available.

The working group will be led by Kristina Nelson and Connor Halleck-Dube.  To participate in this working group, send an email to one of these organizers.

Both students and faculty are encouraged to participate in the working groups.

The project meets Monday - Thursday from 13:00 to 17:00 PDT in Evans 961.

Title:  

Special points and Isogenies in characteristic 0 and characteristic p. 

Abstract: 

 I will contrast the characteristic p and characteristic 0 behaviour of CM abelian varieties and isogenies, mainly focusing on my recent joint work with Kisin-Lam-Srinivasan, as well as forthcoming work with Oswal-Patel-Zhu. Specifically, I will focus on questions pertaining to the liftability of CM points and isogenies, Rapoport-Zink spaces, and how this can be used to understand the non-archimedian geometry of Shimura varieties and the non-archimedian distribution of CM points. 

References:

1. Chai-Oort: moduli of abelian varieties and p-divisible groups (https://webspace.science.uu.nl/~oort0109/CMIPchaioort2.pdf)

2. Kisin-Lam-S-Srinivasan: Finiteness of reductions of Hecke orbits (https://arxiv.org/pdf/2109.05147.pdf)

3. Messing: The crystals associated to Barsotti-Tate groups (https://link.springer.com/book/10.1007/BFb0058301)

4. Oort: Foliations in moduli spaces of abelian varieties: https://www.ams.org/journals/jams/2004-17-02/S0894-0347-04-00449-7/S0894-0347-04-00449-7.pdf

5. Rapoport-Zink: Period spaces for p-divisible groups 

Exercises for working group:

Suggested preparation for the working group:

TBA