#### Vol. 4, No. 2, 2022

 Recent Issues Volume 4, Issue 4 Volume 4, Issue 3 Volume 4, Issue 2 Volume 4, Issue 1 Volume 3, Issue 4 Volume 3, Issue 3 Volume 3, Issue 2 Volume 3, Issue 1 Volume 2, Issue 4 Volume 2, Issue 3 Volume 2, Issue 2 Volume 2, Issue 1 Volume 1, Issue 4 Volume 1, Issue 3 Volume 1, Issue 2 Volume 1, Issue 1
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN (electronic): 2576-7666 ISSN (print): 2576-7658 Author Index To Appear Other MSP Journals
Symplectic geometry of $p$-adic Teichmüller uniformization for ordinary nilpotent indigenous bundles

### Yasuhiro Wakabayashi

Vol. 4 (2022), No. 2, 203–247
##### Abstract

We provide a new aspect of the $p$-adic Teichmüller 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.

##### Keywords
hyperbolic curve, indigenous bundle, symplectic structure, canonical lifting, $p$-adic Teichmüller theory, uniformization, crystal
Primary: 14H10
Secondary: 53D30