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

Günter Harder

ISBN 10: 3834826863 / ISBN 13: 9783834826862

Published by Vieweg+Teubner Verlag, Vieweg+Teubner Verlag, 2014

About this Item

Druck auf Anfrage Neuware - Printed after ordering - In this second volume of 'Lectures on Algebraic Geometry', the author starts with some foundational concepts in the theory of schemes and gives a somewhat casual introduction into commutative algebra. After that he proves the finiteness results for coherent cohomology and discusses important applications of these finiteness results. In the two last chapters, curves and their Jacobians are treated and some outlook into further directions of research is given.The first volume is not necessarily a prerequisite for the second volume if the reader accepts the concepts on sheaf cohomology. On the other hand, the concepts and results in the second volume have been historically inspired by the theory of Riemann surfaces. There is a deep connection between these two volumes, in spirit they form a unity.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.Prof. Dr. Günter Harder, Department of Mathematics, University of Bonn, and Max-Planck-Institute for Mathematics, Bonn, Germany.

Seller Inventory # 9783834826862

Bibliographic Details

• Title: Lectures on Algebraic Geometry II : Basic Concepts, Coherent Cohomology, Curves and their Jacobians
• Publisher: Vieweg+Teubner Verlag, Vieweg+Teubner Verlag
• Publication Date: 2014
• Language: English
• ISBN 10: 3834826863
• ISBN 13: 9783834826862
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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