**Date & Time:** Monday, July 25, 2011, 15:30-16:30.

**Venue:** Ramanujan Hall

**Title:**Generalized Hasse Invariants

**Speaker:**Marc-Hubert Nicole, Institut de MathÃ©matiques de Luminy

**Abstract:**
The classical Hasse invariant is the determinant of the Hasse-Witt matrix. It allows cutting out the ordinary locus within the special fiber of a modular curve: this is the locus where the Hasse invariant is invertible. For more general Shimura varieties, the ordinary locus may be empty, and the Hasse invariant is thus trivially zero. This defect is already visible in dimension one, that is for Shimura curves at primes dividing the discriminant. We shall present generalizations of the Hasse invariant for Shimura varieties which are moduli spaces of abelian varieties with additional structures.