This ebook and the next moment quantity is an creation into glossy algebraic geometry. within the first quantity the equipment of homological algebra, concept of sheaves, and sheaf cohomology are built. those equipment are critical 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 strategies 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 some of the glossy equipment were expected by way of them.
For this moment variation the textual content used to be thoroughly revised and corrected. the writer additionally additional a brief part on moduli of elliptic curves with N-level constructions. This new paragraph anticipates a few of the options of quantity II.
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