The Canonical Subgroup
by
Eyal Goren
McGill University
Coauthors: Payman Kassaei (King's College)

The canonical subgroup plays a crucial role in defining and studying the U operator on overconvergent p-adic modular forms. It has been studied by Lubin and Katz and recently by Abbes-Mokrane, Andreatta-Gasbarri, Conrad, and Kisin-Lai. After a short introduction to p-adic modular forms and some motivation, I shall discuss joint work with P. Kassaei (King's College) on the canonical subgroup for a general class of Shimura varieties. Our approach is different from the methods used by all the authors above in that it relies, in essence, only on the underlying geometry and not its interpretation in terms of moduli of abelian varieties; the test case we shall focus on is that of Hilbert modular varieties.

Date received: May 9, 2008