SCHOTTKY UNIFORMIZATION THEORY ON RIEMANN SURFACES AND MUMFORD CURVESOF INFINITE GENUS

Authors
ICHIKAWA T
Citation
T. Ichikawa, SCHOTTKY UNIFORMIZATION THEORY ON RIEMANN SURFACES AND MUMFORD CURVESOF INFINITE GENUS, Journal fur die Reine und Angewandte Mathematik, 486, 1997, pp. 45-68
Citations number
25
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Journal fur die Reine und Angewandte Mathematik → ACNP
ISSN journal
00754102
Volume
486
Year of publication
1997
Pages
45 - 68
Database
ISI
SICI code
0075-4102(1997)486:<45:SUTORS>2.0.ZU;2-6
Abstract
In this paper, using Schottky uniformization theory over (archimedean and nonarchimedean) local fields, analytic curves (i.e. Riemann surfac es and Mumford curves) of infinite genus are studied. For certain Scho ttky uniformized analytic curves of infinite genus, natural meromorphi c 1-forms and period integrals are constructed. As its application, it is shown that the p-adic theta functions of Mumford curves of infinit e genus generate formal solutions of the KP hierarchy.