Symplectic geometry of p-adic Teichmuller uniformization for ordinary nilpotent indigenous bundles

摘要

We provide a new aspect of the p-adic Teichmuller theory established by Mochizuki. The formal stack classifying p-adic canonical liftings of ordinary nilpotent indigenous bundles embodies a p-adic analogue of uniformization of hyperbolic Riemann surfaces, as well as a hyperbolic analogue of Serre-Tate theory of ordinary abelian varieties. We prove a comparison theorem for the canonical symplectic structure on the cotangent bundle of this formal stack and Goldman's symplectic structure. This result may be thought of as a p-adic analogue of comparison theorems in the theory of projective structures on Riemann surfaces proved by Kawai and other mathematicians.