The Geometry Of Schemes
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The Geometry Of Schemes
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
The Geometry Of Schemes written by David Eisenbud 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 2006-04-06 with Mathematics categories.
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
The Geometry Of Schemes
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Author : David Eisenbud &
language : en
Publisher:
Release Date : 2015-04-15
The Geometry Of Schemes written by David Eisenbud & and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-15 with categories.
The Geometry Of Schemes
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Author : David Eisenbud
language : en
Publisher: Boom Koninklijke Uitgevers
Release Date : 2000
The Geometry Of Schemes written by David Eisenbud and has been published by Boom Koninklijke Uitgevers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
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
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Author : Ulrich Görtz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-06
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 2010-08-06 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.
Introduction To The Theory Of Schemes
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Author : Yuri I. Manin
language : en
Publisher: Springer
Release Date : 2018-05-15
Introduction To The Theory Of Schemes written by Yuri I. Manin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-15 with Mathematics categories.
This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas. "This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson
The Red Book Of Varieties And Schemes
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Author : David Mumford
language : en
Publisher: Springer
Release Date : 2004-02-21
The Red Book Of Varieties And Schemes written by David Mumford and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-21 with Mathematics categories.
Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
Introduction To Affine Group Schemes
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Author : W.C. Waterhouse
language : en
Publisher: Springer Science & Business Media
Release Date : 1979-11-13
Introduction To Affine Group Schemes written by W.C. Waterhouse 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 1979-11-13 with Mathematics categories.
Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.
Basic Algebraic Geometry 2
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Author : Igor R. Shafarevich
language : en
Publisher: Springer
Release Date : 2012-11-27
Basic Algebraic Geometry 2 written by Igor 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 2012-11-27 with Mathematics categories.
The second volume of Shafarevich's introductory book on algebraic varieties and complex manifolds. As with Volume 1, the author has revised the text and added new material, e.g. as a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum, making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as those in theoretical physics.