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Lectures on Algebraic Geometry II: Basic Concepts, Coherent Cohomology, Curves and Their Jacobians
Günter Harder, Max Planck Institute for Mathematics, Bonn, Germany
A publication of Vieweg+Teubner.
cover
Vieweg Aspects of Mathematics
2011; 365 pp; hardcover
Volume: 41
ISBN-10: 3-8348-0432-0
ISBN-13: 978-3-8348-0432-7
List Price: US$89.95
Member Price: US$80.95
Order Code: VWAM/41
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This second volume introduces the concept of schemes, reviews some commutative algebra, and introduces projective schemes. The finiteness theorem for coherent sheaves is proved; here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved.

Finally, the author explores further developments--for instance, étale cohomology--and states some fundamental theorems.

A publication of Vieweg+Teubner. The AMS is exclusive distributor in North America. Vieweg+Teubner Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan.

Readership

Graduate students and research mathematicians interested in algebraic geometry.

Table of Contents

  • Basic concepts of the theory of schemes
  • Some commutative algebra
  • Projective schemes
  • Curves and the theorem of Riemann-Roch
  • The Picard functor for curves and Jacobians
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