by Eberhard Freitag (Author)
The book contains an introduction into the theory of Riemann surfaces using a sheaf theoretic approach. Sheaf theory is developed completely. The cohomology of sheaves is introduced by means of the canonical flabby resolution of Godement. The Riemann-Roch theorem is proved for vector bundles. Abel's theorem and the Jacobi inversion theorem are treated. As application, dimension formulae for vector valued automorphic forms in one variable are proved. The necessary tools from topology and algebra are described completely but highly focussed.
Author Biography
The author is Professor at the mathematical departement of the University of Heidelberg. He is expert in the theory of automorphic forms of several variables. Besides many research papers, he published several books in the Springer publishing house about Siegel modular functions (available also in Japanese language), Hilbert modular functions, singular modular forms, two volumes about Complex Analysis (the first volume in joint work with Rolf Busam). These volumes are also available in German language. In joint work with Reinhardt Kiehl a book about the Weil conjectures appeared.