## Speaker:

Marc-Hubert Nicole

## Institution:

Institut mathématique de Luminy / UCLA

## Time:

Tuesday, October 28, 2014 - 2:00pm to 3:00pm

## Location:

RH340P

Let $p>2$ be a prime number. The classical Hasse invariant is a modular form modulo p that vanishes on the supersingular points of a modular curve. Its non-zero locus is called the ordinary locus. While the Hasse invariant generalizes easily to moduli spaces of abelian varieties with additional structures, it happens often that the generalized ordinary locus is empty, and therefore the Hasse invariant is then tautologically trivial. We present an elementary and natural generalization of the Hasse invariant, which is always non-trivial, and which enjoys essentially all the same properties as the classical Hasse invariant. In particular, the usual applications generalize nicely, and we shall highlight the state-of-the-art in our talk.