Lectures on Algebraic Geometry II Basic Concepts, Coherent Cohomolog
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 cohere
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Günter Harder
Lectures on Algebraic Geometry II Basic Concepts, Coherent Cohomology, Curves and their Jacobians
Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de.
Prof. Dr. Günter Harder Max-Planck-Institute for Mathematics Vivatsgasse 7 53111 Bonn Germany [email protected]
Mathematics Subject Classification 14-01, 14A01, 14F01, 14H01, 14K01
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Preface This is now, at last, the second volume of my ”Lectures on Algebraic Geometry”. When working on this second volume, I always had a saying by Peter Gabriel on my mind: ”Der Weg zur H¨olle ist mit zweiten B¨anden gepflastert!” (The path to hell is paved with (never written?) second volumes.) Very often I felt like Sisyphos in Homer’s Oddyssea. Sisyphos tries to push a rock over the ridge and just before he reaches top the rock rolls down again. Only at this very moment, when I am writing this preface, I am gaining some confidence that this second volume finally may come to life. It is still valid what I said in the preface to the first volume, I plan to write a book on Cohomology of arithmetic groups. Actually there exists a very preliminary version of this ”Volume III” on my home page at the Bonn university. The present book is also meant to provide background for ”VolumeIII”. ”Volume III” will be different in nature, we do not give an introduction into a field which is well established and already treated in other text books. It will rather be a description of a research area which is still developing, it will contain some new results, and it will put old results into a new perspective. I will formulate open questions and formulate problems, which are important on one hand but which are also tractable. The first group of fundamental results in this book is proved in Chapter 8 when I discuss the finiteness results for the cohomology of coherent sheaves and the semi-continuity theorems. Here I use the theorems on sheaf cohomology which are proved in the first volume. I pu
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