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Author : Renaud Gauthier
Publisher :
ISBN 13 : 9781387953042
Total Pages : 0 pages
Book Rating : 4.9/5 (53 download)
Download or read book Elements of Derived Algebraic Geometry written by Renaud Gauthier and published by . This book was released on 2022-05-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dennis Gaitsgory
Publisher : American Mathematical Society
ISBN 13 : 1470452847
Total Pages : 533 pages
Book Rating : 4.4/5 (74 download)
Download or read book A Study in Derived Algebraic Geometry written by Dennis Gaitsgory and published by American Mathematical Society. This book was released on 2019-12-31 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a “renormalization” of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of $infty$-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the $mathrm{(}infty, 2mathrm{)}$-category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on $mathrm{(}infty, 2mathrm{)}$-categories needed for the third part.
Author : Dennis Gaitsgory
Publisher : American Mathematical Society
ISBN 13 : 1470452855
Total Pages : 436 pages
Book Rating : 4.4/5 (74 download)
Download or read book A Study in Derived Algebraic Geometry written by Dennis Gaitsgory and published by American Mathematical Society. This book was released on 2020-10-07 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry. To that end, it introduces the notion of inf-scheme, which is an infinitesimal deformation of a scheme and studies ind-coherent sheaves on such. As an application of the general theory, the six-functor formalism for D-modules in derived geometry is obtained. This volume consists of two parts. The first part introduces the notion of ind-scheme and extends the theory of ind-coherent sheaves to inf-schemes, obtaining the theory of D-modules as an application. The second part establishes the equivalence between formal Lie group(oids) and Lie algebr(oids) in the category of ind-coherent sheaves. This equivalence gives a vast generalization of the equivalence between Lie algebras and formal moduli problems. This theory is applied to study natural filtrations in formal derived geometry generalizing the Hodge filtration.
Author : Dennis Gaitsgory
Publisher :
ISBN 13 : 9781470435684
Total Pages : 1016 pages
Book Rating : 4.4/5 (356 download)
Download or read book A Study in Derived Algebraic Geometry written by Dennis Gaitsgory and published by . This book was released on 2017-08-30 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This two-volume monograph develops generalization of various topics in algebraic geometry in the context derived algebraic geometry. Volume 1 presents the theory of ind-coherent sheaves, which are a ``renormalization'' of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. Volume 2 develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry. To that end, it introduces the notion of inf-scheme, which is an infinitesimal deformation of a scheme and studies ind-coherent sheaves on inf-schemes. As an application of the general theory, the six-functor formalism for D-modules in derived geometry is obtained.
Author : Dennis Gaitsgory
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (128 download)
Download or read book A Study in Derived Algebraic Geometry written by Dennis Gaitsgory and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Derived Algebraic Geometry written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria for the representability of a moduli functor by geometric objects of these types.
Author : Jacob Lurie
Publisher :
ISBN 13 :
Total Pages : 193 pages
Book Rating : 4.:/5 (56 download)
Download or read book Derived Algebraic Geometry written by Jacob Lurie and published by . This book was released on 2004 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria for the representability of a moduli functor by geometric objects of these types.
Author : Bertrand Toën
Publisher : American Mathematical Soc.
ISBN 13 : 0821840991
Total Pages : 242 pages
Book Rating : 4.8/5 (218 download)
Download or read book Homotopical Algebraic Geometry II: Geometric Stacks and Applications written by Bertrand Toën and published by American Mathematical Soc.. This book was released on 2008 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.
Author : Dennis Gaitsgory
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (21 download)
Download or read book A Study in Derived Algebraic Geometry: Correspondences and duality written by Dennis Gaitsgory and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a ``renormalization'' of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of $\infty$-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the $\mathrm{(}\infty, 2\mathrm{)}$-category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on $\mathrm{(}\infty, 2\mathrm{)}$-categories needed for the third part.
Author : Lin Weng
Publisher : World Scientific
ISBN 13 : 981256814X
Total Pages : 411 pages
Book Rating : 4.8/5 (125 download)
Download or read book Arithmetic Geometry and Number Theory written by Lin Weng and published by World Scientific. This book was released on 2006 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.
Author : Dennis Gaitsgory
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (21 download)
Download or read book A Study in Derived Algebraic Geometry: Deformations, Lie theory, and formal geometry written by Dennis Gaitsgory and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a ``renormalization'' of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of $\infty$-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the $\mathrm{(}\infty, 2\mathrm{)}$-category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on $\mathrm{(}\infty, 2\mathrm{)}$-categories needed for the third part.
Author : Annette Huber
Publisher : Springer
ISBN 13 : 3540492747
Total Pages : 216 pages
Book Rating : 4.5/5 (44 download)
Download or read book Mixed Motives and their Realization in Derived Categories written by Annette Huber and published by Springer. This book was released on 2006-11-17 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives via their well-defined realizations. This includes a review of several known cohomology theories. A new absolute cohomology is introduced and studied. The book assumes knowledge of the standard cohomological techniques in algebraic geometry as well as K-theory. So the monograph is primarily intended for researchers. Advanced graduate students can use it as a guide to the literature.
Author : Renaud Gauthier
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311133421X
Total Pages : 489 pages
Book Rating : 4.1/5 (113 download)
Download or read book Derived Algebraic Geometry written by Renaud Gauthier and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-01-29 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Emil Artin
Publisher :
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.F/5 ( download)
Download or read book Elements of Algebraic Geometry written by Emil Artin and published by . This book was released on 1955 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : André Weil
Publisher :
ISBN 13 : 9781470431761
Total Pages : 363 pages
Book Rating : 4.4/5 (317 download)
Download or read book Foundations of Algebraic Geometry written by André Weil and published by . This book was released on 1946 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Author : David Eisenbud
Publisher : Springer Science & Business Media
ISBN 13 : 0387226397
Total Pages : 265 pages
Book Rating : 4.3/5 (872 download)
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 265 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.
Author : James R. Munkres
Publisher : CRC Press
ISBN 13 : 0429962460
Total Pages : 465 pages
Book Rating : 4.4/5 (299 download)
Download or read book Elements Of Algebraic Topology written by James R. Munkres and published by CRC Press. This book was released on 2018-03-05 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.
