Lectures on Algebraic Geometry II: Basic Concepts, Coherent Cohomology, Curves a

Description: Lectures on Algebraic Geometry II by GÜnter Harder, Klas Diederich This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 etale cohomology- and states some fundamental theorems. Notes 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. Back Cover 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. G Author Biography Prof. Dr. GÜnter Harder, Max-Planck-Institute for Mathematics, Bonn 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 Promotional Abel, Jacobi and Riemann from todays point of view. Promotional "Headline" Abel, Jacobi and Riemann from todays point of view. Feature Algebraische Geometrie: Von Abel und Riemann bis heute Description for Sales People 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 Details ISBN3834804320 Short Title LECTURES ON ALGEBRAIC GEOMETRY Series Aspects of Mathematics Language English ISBN-10 3834804320 ISBN-13 9783834804327 Media Book Format Hardcover Series Number 39 Subtitle Basic Concepts, Coherent Cohomology, Curves and their Jacobians Year 2011 Publication Date 2011-04-05 Pages 365 Imprint Vieweg+Teubner Verlag Place of Publication Weisbaden Country of Publication Germany Translated from German Edition 2011th DOI 10.1007/978-3-8348-8159-5 UK Release Date 2011-04-05 Illustrations XIII, 365 p. Author Klas Diederich Publisher Springer Fachmedien Wiesbaden Edition Description 2011 ed. Alternative 9783834826862 DEWEY 516.35 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:127855667;

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