This ebook and the subsequent moment quantity is an creation into sleek algebraic geometry. within the first quantity the tools of homological algebra, concept of sheaves, and sheaf cohomology are built. those tools are fundamental for contemporary algebraic geometry, yet also they are basic 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 speculation 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 few of the smooth tools were expected by means of them.
For this moment variation the textual content was once thoroughly revised and corrected. the writer additionally additional a brief part on moduli of elliptic curves with N-level buildings. This new paragraph anticipates a number of the thoughts of quantity II.
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