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Symplectic geometry
of $p$-adic Teichmüller uniformization for ordinary nilpotent
indigenous bundles
Yasuhiro Wakabayashi |
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Vol. 4 (2022), No. 2, 203–247
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Abstract |
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We provide a new aspect of the -adic Teichmüller theory established by Mochizuki. The formal stack classifying -adic canonical liftings of ordinary nilpotent indigenous bundles embodies a -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 -adic analogue of comparison theorems in the theory of projective structures on Riemann surfaces proved by Kawai and other mathematicians. |
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Keywords
hyperbolic curve, indigenous bundle, symplectic structure,
canonical lifting, $p$-adic Teichmüller theory,
uniformization, crystal
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Mathematical Subject Classification
Primary: 14H10
Secondary: 53D30
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Milestones
Received: 19 May 2020
Revised: 26 September 2021
Accepted: 11 October 2021
Published: 24 August 2022
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Authors |
| Yasuhiro Wakabayashi | |
| Department of Mathematics Tokyo Institute of Technology Ookayama, Meguro-ku Tokyo Japan |
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