Lectures on Algebraic Geometry - 2: Basic Concepts, Coherent Cohomology, Curves and their Jacobians

This second volume introduces the concept of shemes, 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 gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.

About the author

Prof. Dr. Günter Harder, Max-Planck-Institute for Mathematics, Bonn

Summary

This second volume introduces the concept of shemes, 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 gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.

Product details

• Authors: Günter Harder
• Assisted by: Kla Diederich (Editor), Klas Diederich (Editor), Klas Diederich (Editor of the series)
• Publisher: Vieweg+Teubner
• Content: Book
• Product form: Hardback
• Publication date: 11.05.2011
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra
• EAN: 9783834804327
• ISBN: 978-3-8348-0432-7
• Pages: 365
• Illustrations: XIII, 365 p.
• Dimensions (packing): 17.7 x 24.9 x 2.5 cm
• Weight (packing): 806 g
• Set: Lectures on Algebraic Geometry > 2; Lectures on Algebraic Geometry > 2
• Series: Aspects of Mathematics > 39; Aspects of Mathematics
• Subjects: Geometrie : Lehrwerke; Algebra; Mathematics and Statistics; Kommutative Algebra; sheaves