This publication and the next moment quantity is an advent into smooth algebraic geometry. within the first quantity the equipment of homological algebra, thought of sheaves, and sheaf cohomology are constructed. those tools are necessary for contemporary algebraic geometry, yet also they are primary for different branches of arithmetic and of significant curiosity of their own.
within the final bankruptcy of quantity I those options are utilized to the speculation of compact Riemann surfaces. during this bankruptcy the writer makes transparent how influential the guidelines of Abel, Riemann and Jacobi have been and that a few of the sleek equipment were expected via them.
For this moment variation the textual content used to be thoroughly revised and corrected. the writer additionally extra a quick part on moduli of elliptic curves with N-level constructions. This new paragraph anticipates many of the options of quantity II.
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