Séminaire d'arithmétique à Lyon

Incompressibility of Galois covers beyond the ordinary case

par Dr Najmuddin Fakhruddin

Europe/Paris
Description

In a recent article, Farb, Kisin and Wolfson proved that principal

p-congruence covers of Siegel modular varieties (and certain subvarieties

thereof) are incompressible, i.e., are not (rationally) the base change of covers

of lower dimensional varieties. In joint work with Patrick Brosnan we

found a different proof, which also applies to some exceptional Shimura

varieties, and our results suggest that incompressibility should hold for

all Shimura varieties and almost all primes p. In my talk I will discuss the

case of p-congruence covers of some unitary Shimura varieties for primes

p at which the special fibre of Kottwitz's integral model has no ordinary points.

(Based on joint work with Rijul Saini.)