Conformal and quasiconformal categorical representation of hyperbolic Riemann surfaces

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概要

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• In this paper, we consider various categories of hyperbolic Riemann surfaces and show, in various cases, that the {\it conformal} or {\it quasiconformal} structure of the Riemann surface may be reconstructed, up to possible confusion between holomorphic and anti-holomorphic structures, in a natural way from such a category. The theory exposed in the present paper is motivated partly by a classical result concerning the categorical representation of sober topological spaces, partly by previous work of the author concerning the categorical representation of arithmetic log schemes, and partly by a certain {\it analogy with $p$-adic anabelian geometry} --- an analogy which the theory of the present paper serves to render more explicit.

• 広島大学の論文

著者

• Mochizuki Shinichi

  Research Institute For Mahematical Sciences Kyoto University

関連論文

• The Etale Theta Function and Its Frobenioid-Theoretic Manifestations
• The Geometry of Anabelioids
• Conformal and quasiconformal categorical representation of hyperbolic Riemann surfaces
• The Geometry of the Compactification of the Hurwitz Scheme
• On Semi-Positivity and Filtered Frobenius Crystals
• A combinatorial version of the Grothendieck conjecture
• Semi-graphs of Anabelioids
• A Theory of Ordinary $p$-Adic Curves
• The Profinite Grothendieck Conjecture for Closed Hyperbolic Curves over Number Fields

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