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Algebraic Geometry Ii Cohomology Of Schemes
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Book Synopsis Algebraic Geometry II: Cohomology of Schemes by : Ulrich Görtz
Download or read book Algebraic Geometry II: Cohomology of Schemes written by Ulrich Görtz and published by Springer Nature. This book was released on 2023-11-22 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Geometry 2 by : Kenji Ueno
Download or read book Algebraic Geometry 2 written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 1999 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Geometry by : Ulrich Görtz
Download or read book Algebraic Geometry written by Ulrich Görtz and published by Springer Science & Business Media. This book was released on 2010-08-09 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Geometry I: Schemes by : Ulrich Görtz
Download or read book Algebraic Geometry I: Schemes written by Ulrich Görtz and published by Springer Nature. This book was released on 2020-07-27 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Geometry II by : David Mumford
Download or read book Algebraic Geometry II written by David Mumford and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Algebraic Geometry II by : Günter Harder
Download or read book Lectures on Algebraic Geometry II written by Günter Harder and published by Springer Science & Business Media. This book was released on 2011-04-21 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Geometry by : Robin Hartshorne
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Book Synopsis The Geometry of Schemes by : David Eisenbud
Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Etale Cohomology (PMS-33) by : J. S. Milne
Download or read book Etale Cohomology (PMS-33) written by J. S. Milne and published by Princeton University Press. This book was released on 1980-04-21 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Algebraic Geometry and Arithmetic Curves by : Qing Liu
Download or read book Algebraic Geometry and Arithmetic Curves written by Qing Liu and published by Oxford University Press. This book was released on 2006-06-29 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.
Book Synopsis Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry by : Jean H. Gallier
Download or read book Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry written by Jean H. Gallier and published by World Scientific Publishing Company. This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homology and cohomology -- De Rham cohomology -- Singular homology and cohomology -- Simplicial homology and cohomology -- Homology and cohomology of CW complexes -- Poincaré duality -- Presheaves and sheaves; Basics -- Cech cohomology with values in a presheaf -- Presheaves and sheaves; A deeper look -- Derived functors, [delta]-functors, and [del]-functors -- Universal coefficient theorems -- Cohomology of sheaves -- Alexander and Alexander-Lefschetz duality -- Spectral sequences.
Book Synopsis Algebraic Geometry II by : I.R. Shafarevich
Download or read book Algebraic Geometry II written by I.R. Shafarevich and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Geometry 1 written by 健爾·上野 and published by American Mathematical Soc.. This book was released on 1999 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.
Book Synopsis Geometry and Topology of Configuration Spaces by : Edward R. Fadell
Download or read book Geometry and Topology of Configuration Spaces written by Edward R. Fadell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: With applications in mind, this self-contained monograph provides a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres, making the subject accessible to researchers and graduates with a minimal background in classical homotopy theory and algebraic topology.
Book Synopsis Algebraic Geometry by : Daniel Perrin
Download or read book Algebraic Geometry written by Daniel Perrin and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
Book Synopsis Lectures on Algebraic Geometry I by : Günter Harder
Download or read book Lectures on Algebraic Geometry I written by Günter Harder and published by Springer Science & Business Media. This book was released on 2008-08-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
Book Synopsis Manifolds, Sheaves, and Cohomology by : Torsten Wedhorn
Download or read book Manifolds, Sheaves, and Cohomology written by Torsten Wedhorn and published by Springer. This book was released on 2016-07-25 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
