Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic geometry of $p$-adic Teichm\"{u}ller uniformization for
  ordinary nilpotent indigenous bundles   The aim of the present paper is to provide a new aspect of the $p$-adic
Teichm\"{u}ller theory established by S. Mochizuki. We study the symplectic
geometry of the $p$-adic formal stacks $\widehat{\mathcal{M}}_{g,
\mathbb{Z}_p}$ (= the moduli classifying $p$-adic formal curves of fixed genus
$g>1$) and $\widehat{\mathcal{S}}_{g, \mathbb{Z}_p}$ (= the moduli classifying
$p$-adic formal curves of genus $g$ equipped with an indigenous bundle). A
major achievement in the (classical) $p$-adic Teichm\"{u}ller theory is the
construction of the locus $\widehat{\mathcal{N}}_{g,
\mathbb{Z}_p}^{\mathrm{ord}}$ in $\widehat{\mathcal{S}}_{g, \mathbb{Z}_p}$
classifying $p$-adic canonical liftings of ordinary nilpotent indigenous
bundles. The formal stack $\widehat{\mathcal{N}}_{g,
\mathbb{Z}_p}^{\mathrm{ord}}$ 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. In the present paper, the canonical
symplectic structure on the cotangent bundle $T^\vee_{\mathbb{Z}_p}
\widehat{\mathcal{M}}_{g, \mathbb{Z}_p}$ of $\widehat{\mathcal{M}}_{g,
\mathbb{Z}_p}$ is compared to Goldman's symplectic structure defined on
$\widehat{\mathcal{S}}_{g, \mathbb{Z}_p}$ after base-change by the projection
$\widehat{\mathcal{N}}_{g, \mathbb{Z}_p}^{\mathrm{ord}} \rightarrow
\widehat{\mathcal{M}}_{g, \mathbb{Z}_p}$. We can think of this comparison as a
$p$-adic analogue of certain results in the theory of projective structures on
Riemann surfaces proved by S. Kawai and other mathematicians.

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The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn