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2022 Symplectic geometry of p-adic Teichmüller uniformization for ordinary nilpotent indigenous bundles
Yasuhiro Wakabayashi
Tunisian J. Math. 4(2): 203-247 (2022). DOI: 10.2140/tunis.2022.4.203

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.

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Yasuhiro Wakabayashi. "Symplectic geometry of p-adic Teichmüller uniformization for ordinary nilpotent indigenous bundles." Tunisian J. Math. 4 (2) 203 - 247, 2022. https://doi.org/10.2140/tunis.2022.4.203

Information

Received: 19 May 2020; Revised: 26 September 2021; Accepted: 11 October 2021; Published: 2022
First available in Project Euclid: 2 September 2022

Digital Object Identifier: 10.2140/tunis.2022.4.203

Subjects:
Primary: 14H10
Secondary: 53D30

Keywords: canonical lifting , crystal , hyperbolic curve , indigenous bundle , p-adic Teichmüller theory , symplectic structure , uniformization

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.4 • No. 2 • 2022
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