特別講演 / Lecture
The Hitchin-Mochizuki Morphism
June 3 (Fri), 2011, 11:00-12:00
RIMS, Room 206
Kirti JOSHI (University of Arizona, USA)
S. Mochizuki in his foundational work on p-adic uniformization of curves initiated the study of indigenous vector bundles of rank two in positive characteristic and defined a natural morphism from the space of such bundles to the space of quadratic differentials. In this talk I will explain a part of my recent joint work with C. Pauly where we provide a natural generalization of this morphism (which we call the Hitchin-Mochizuki morphism) to opers, which are natural generalizations of indigenous bundles to higher ranks.
On p-adic differential equations, q-difference equations, Galois representations and Hasse-Arf filtrations
January 31 (Mon), 2005, 15:00-17:00
RIMS, Room 206
Yves ANDRE (Ecole Normale Superieure, France)
We shall first sketch two relatively well-known analogies: between differential equations and q-difference equations on one hand, and between Galois representations of local fields of characteristic p and complex linear differential equations over a punctured disk on the other hand. In the p-adic world, it turns out that both analogies can be substantially strengthened, and we shall explain how they eventually lead to some equivalences of categories. The three categories under consideration carry natural filtrations of ``Hasse-Arf type", which turn out to correspond to each other despite their very different natures. A byproduct of the theory is that every p-adic differential module defined over an infinitesimally thin annulus of outer radius one, and which is invariant (up to isomorphism) under raising the variable x to the p-th power, can be canonically deformed into a family of q-difference modules over the annulus, parametrized by a p-adic number q close to 1. In this family, the fibre at q is isomorphic to the image of the fiber at q^p under raising the variable x to the p-th power.