By Günter Harder
This publication and the next moment quantity is an advent into smooth algebraic geometry. within the first quantity the equipment of homological algebra, conception of sheaves, and sheaf cohomology are constructed. those equipment are vital for contemporary algebraic geometry, yet also they are basic for different branches of arithmetic and of significant curiosity of their personal. within the final bankruptcy of quantity I those techniques are utilized to the idea of compact Riemann surfaces. during this bankruptcy the writer makes transparent how influential the tips of Abel, Riemann and Jacobi have been and that the various glossy tools were expected by means of them. For this moment version the textual content used to be thoroughly revised and corrected. the writer additionally extra a brief part on moduli of elliptic curves with N-level buildings. This new paragraph anticipates the various innovations of quantity II.
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