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November 2006 Conformal and quasiconformal categorical representation of hyperbolic Riemann surfaces
Shinichi Mochizuki
Hiroshima Math. J. 36(3): 405-441 (November 2006). DOI: 10.32917/hmj/1171377082

Abstract

In this paper, we consider various categories of hyperbolic Riemann surfaces and show, in various cases, that the conformal or 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 analogy with $p$-adic anabelian geometry --- an analogy which the theory of the present paper serves to render more explicit.

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Shinichi Mochizuki. "Conformal and quasiconformal categorical representation of hyperbolic Riemann surfaces." Hiroshima Math. J. 36 (3) 405 - 441, November 2006. https://doi.org/10.32917/hmj/1171377082

Information

Published: November 2006
First available in Project Euclid: 13 February 2007

zbMATH: 1124.14031
MathSciNet: MR2290666
Digital Object Identifier: 10.32917/hmj/1171377082

Subjects:
Primary: 14H55, 30F60

Rights: Copyright © 2006 Hiroshima University, Mathematics Program

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Vol.36 • No. 3 • November 2006
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