Algebraic Geometry Ii Cohomology Of Schemes
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Algebraic Geometry Ii Cohomology Of Schemes
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Author : Ulrich Görtz
language : en
Publisher: Springer Nature
Release Date : 2023-11-22
Algebraic Geometry Ii Cohomology Of Schemes written by Ulrich Görtz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-22 with Mathematics categories.
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.
Lectures On Algebraic Geometry Ii
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Author : Günter Harder
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-21
Lectures On Algebraic Geometry Ii written by Günter Harder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-21 with Mathematics categories.
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.
Algebraic Geometry Ii
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Author : I.R. Shafarevich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22
Algebraic Geometry Ii written by I.R. Shafarevich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Mathematics categories.
This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.
Algebraic Geometry I Schemes
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Author : Ulrich Görtz
language : en
Publisher: Springer Nature
Release Date : 2020-07-27
Algebraic Geometry I Schemes written by Ulrich Görtz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-27 with Mathematics categories.
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.
Algebraic Geometry 2
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Author : Kenji Ueno
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Algebraic Geometry 2 written by Kenji Ueno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes. In this volume, the author turns to the theory of sheaves and their cohomology. A sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves.
Algebraic Geometry
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Author : Ulrich Görtz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-09
Algebraic Geometry written by Ulrich Görtz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-09 with Mathematics categories.
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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Author : I. R. Shafarevich
language : en
Publisher:
Release Date : 2007
written by I. R. Shafarevich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Algebraic varieties categories.
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Algebraic Geometry Ii
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Author : I.R. Shafarevich
language : en
Publisher: Springer
Release Date : 2014-10-05
Algebraic Geometry Ii written by I.R. Shafarevich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-05 with Mathematics categories.
This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.
Algebraic Geometry Ii
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Author : David Mumford
language : en
Publisher:
Release Date : 2015
Algebraic Geometry Ii written by David Mumford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Algebraic varieties categories.
Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. This book contains what Mumford had intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added.
Algebraic Geometry Two
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Author : Игорь Ростиславович Шафаревич
language : en
Publisher: Springer Verlag
Release Date : 1996
Algebraic Geometry Two written by Игорь Ростиславович Шафаревич and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This EMS volume consists of two parts. The first part is devoted to cohomology of algebraic varieties. The second part deals with algebraic surfaces. The authors, who are well-known experts in the field, have taken pains to present the material rigorously and coherently. The book contains numerous examples and insights on various topics. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetical algebraic geometry, complex analysis and related fields.