This booklet and the next moment quantity is an creation into glossy algebraic geometry. within the first quantity the equipment of homological algebra, conception of sheaves, and sheaf cohomology are built. those tools are imperative for contemporary algebraic geometry, yet also they are primary for different branches of arithmetic and of serious curiosity of their own.
within the final bankruptcy of quantity I those suggestions 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 a number of the sleek equipment were expected via them.
For this moment variation the textual content was once thoroughly revised and corrected. the writer additionally extra a brief part on moduli of elliptic curves with N-level constructions. This new paragraph anticipates a number of the suggestions of quantity II.
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