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Lectures on Algebraic Geometry II: Basic Concepts, Coherent Cohomology, Curves and their Jacobians (Aspects of Mathematics, 39) - Softcover
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.
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About the Author
Prof. Dr. Günter Harder, Max-Planck-Institute for Mathematics, Bonn
From the 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. Günter Harder, Department of Mathematics, University of Bonn, and Max-Planck-Institute for Mathematics, Bonn, Germany.
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Lectures on Algebraic Geometry II
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 365 pp. Englisch. Seller Inventory # 9783834826862
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Algebraische Geometrie: Von Abel und Riemann bis heuteProf. Dr. Guenter Harder, Max-Planck-Institute for Mathematics, BonnThis second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The fin. Seller Inventory # 11813284
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Lectures on Algebraic Geometry II : Basic Concepts, Coherent Cohomology, Curves and their Jacobians
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Taschenbuch. Condition: Neu. 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
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Straße 46, 65189 Wiesbaden 380 pp. Englisch. Seller Inventory # 9783834826862
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Lectures on Algebraic Geometry II: Basic Concepts, Coherent.
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