Home eBooks Download › a study in derived algebraic geometry

A Study In Derived Algebraic Geometry

Download A Study In Derived Algebraic Geometry PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Study In Derived Algebraic Geometry book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

A Study In Derived Algebraic Geometry

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Dennis Gaitsgory
language : en
Publisher: American Mathematical Society
Release Date : 2019-12-31

A Study In Derived Algebraic Geometry written by Dennis Gaitsgory and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-31 with Mathematics categories.

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.

A Study In Derived Algebraic Geometry

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Dennis Gaitsgory
language : en
Publisher: American Mathematical Society
Release Date : 2020-10-07

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.

A Study In Derived Algebraic Geometry

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Dennis Gaitsgory
language : en
Publisher:
Release Date : 2017

A Study In Derived Algebraic Geometry written by Dennis Gaitsgory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

A Study In Derived Algebraic Geometry

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Dennis Gaitsgory
language : en
Publisher:
Release Date : 2017-08-30

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.

Derived Categories In Algebraic Geometry

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Yujiro Kawamata
language : en
Publisher: Amer Mathematical Society
Release Date : 2012

Derived Categories In Algebraic Geometry written by Yujiro Kawamata and has been published by Amer Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

The study of derived categories is a subject that attracts increasingly many mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory, and mathematical physics. The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic geometry such as the duality theorem. In the 1970s, Beilinson, Gelfand, and Gelfand discovered that a derived category of an algebraic variety may be equivalent to that of a finite-dimensional non-commutative algebra, and Mukai found that there are non-isomorphic algebraic varieties that have equivalent derived categories. In this way, the derived category provides a new concept that has many incarnations. In the 1990s, Bondal and Orlov uncovered an unexpected parallelism between the derived categories and the birational geometry. Kontsevich's homological mirror symmetry provided further motivation for the study of derived categories. This book contains the proceedings of a conference held at the University of Tokyo in January 2011 on the current status of the research on derived categories related to algebraic geometry. Most articles are survey papers on this rapidly developing field. The book is suitable for mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.

Homotopical Algebraic Geometry Ii Geometric Stacks And Applications

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Bertrand Toën
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Homotopical Algebraic Geometry Ii Geometric Stacks And Applications written by Bertrand Toën 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 2008 with Mathematics categories.

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.

Mitteilungen Der Handwerkskammer Bielefeld

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author :
language : en
Publisher:
Release Date : 1947

Mitteilungen Der Handwerkskammer Bielefeld written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with categories.

Derived Categories

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Amnon Yekutieli
language : en
Publisher: Cambridge University Press
Release Date : 2019-12-19

Derived Categories written by Amnon Yekutieli and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-19 with Mathematics categories.

There have been remarkably few systematic expositions of the theory of derived categories since its inception in the work of Grothendieck and Verdier in the 1960s. This book is the first in-depth treatment of this important component of homological algebra. It carefully explains the foundations in detail before moving on to key applications in commutative and noncommutative algebra, many otherwise unavailable outside of research articles. These include commutative and noncommutative dualizing complexes, perfect DG modules, and tilting DG bimodules. Written with graduate students in mind, the emphasis here is on explicit constructions (with many examples and exercises) as opposed to axiomatics, with the goal of demystifying this difficult subject. Beyond serving as a thorough introduction for students, it will serve as an important reference for researchers in algebra, geometry and mathematical physics.

Semi Infinite Algebraic Geometry Of Quasi Coherent Sheaves On Ind Schemes

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Leonid Positselski
language : en
Publisher: Springer Nature
Release Date : 2023-10-16

Semi Infinite Algebraic Geometry Of Quasi Coherent Sheaves On Ind Schemes written by Leonid Positselski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-16 with Mathematics categories.

Semi-Infinite Geometry is a theory of "doubly infinite-dimensional" geometric or topological objects. In this book the author explains what should be meant by an algebraic variety of semi-infinite nature. Then he applies the framework of semiderived categories, suggested in his previous monograph titled Homological Algebra of Semimodules and Semicontramodules, (Birkhäuser, 2010), to the study of semi-infinite algebraic varieties. Quasi-coherent torsion sheaves and flat pro-quasi-coherent pro-sheaves on ind-schemes are discussed at length in this book, making it suitable for use as an introduction to the theory of quasi-coherent sheaves on ind-schemes. The main output of the homological theory developed in this monograph is the functor of semitensor product on the semiderived category of quasi-coherent torsion sheaves, endowing the semiderived category with the structure of a tensor triangulated category. The author offers two equivalent constructions of the semitensor product, as well as its particular case, the cotensor product, and shows that they enjoy good invariance properties. Several geometric examples are discussed in detail in the book, including the cotangent bundle to an infinite-dimensional projective space, the universal fibration of quadratic cones, and the important popular example of the loop group of an affine algebraic group.

C Algebraic Geometry With Corners

DOWNLOAD
AUDIOBOOK
READ ONLINE
Author : Kelli Francis-Staite
language : en
Publisher: Cambridge University Press
Release Date : 2023-12-31

C Algebraic Geometry With Corners written by Kelli Francis-Staite and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-31 with Mathematics categories.

Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.

A Study In Derived Algebraic Geometry

Recent Posts