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An arithmetic Riemann-Roch theorem for metrics with cusps. (English) Zbl 1177.14052

Berichte aus der Mathematik. Aachen: Shaker Verlag; Berlin: Humboldt-Univ., Mathematisch-Naturwissenschaftliche Fakultät (Diss.) (ISBN 978-3-8322-8231-8/hbk). x, 103 p. (2009).
The aim of this Ph.D. thesis is to prove an arithmetic Riemann-Roch theorem in degree one for the canonical line bundle on an arithmetic surface equipped with a metric which is allowed to have a finite number of hyperbolic cusps.

MSC:

14G40 Arithmetic varieties and schemes; Arakelov theory; heights
11-02 Research exposition (monographs, survey articles) pertaining to number theory
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
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