Torsten Wedhorn's Books

Manifolds, Sheaves, and Cohomology

By: Torsten Wedhorn

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Manifolds, Sheaves, and Cohomology

By: Torsten Wedhorn

This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.

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Page Count

366

Publisher

Springer

Published Date

ISBN 10

3658106336

ISBN 13

9783658106331

Algebraic Geometry

Part I: Schemes. With Examples and Exercises

By: Ulrich Görtz,Torsten Wedhorn

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Algebraic Geometry

Part I: Schemes. With Examples and Exercises

By: Ulrich Görtz,Torsten Wedhorn

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

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Page Count

622

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3834897221

ISBN 13

9783834897220

Algebraic Geometry I: Schemes

With Examples and Exercises

By: Ulrich Görtz,Torsten Wedhorn

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Algebraic Geometry I: Schemes

With Examples and Exercises

By: Ulrich Görtz,Torsten Wedhorn

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Page Count

634

Publisher

Springer Nature

Published Date

ISBN 10

3658307331

ISBN 13

9783658307332

Algebraic Geometry II: Cohomology of Schemes

With Examples and Exercises

By: Ulrich Görtz,Torsten Wedhorn

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Algebraic Geometry II: Cohomology of Schemes

With Examples and Exercises

By: Ulrich Görtz,Torsten Wedhorn

This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.

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