Algebraic Spaces and Stacks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Spaces and Stacks write by Martin Olsson. This book was released on 2016-05-13. Algebraic Spaces and Stacks available in PDF, EPUB and Kindle. This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
Stacks and Categories in Geometry, Topology, and Algebra
Stacks and Categories in Geometry, Topology, and Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stacks and Categories in Geometry, Topology, and Algebra write by Tony Pantev. This book was released on 2015-06-26. Stacks and Categories in Geometry, Topology, and Algebra available in PDF, EPUB and Kindle. This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France. Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains. Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.
Stacks and Categories in Geometry, Topology, and Algebra
Stacks and Categories in Geometry, Topology, and Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stacks and Categories in Geometry, Topology, and Algebra write by Tony Pantev. This book was released on 2015. Stacks and Categories in Geometry, Topology, and Algebra available in PDF, EPUB and Kindle. This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France. Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains. Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way
Introduction to Algebraic Geometry and Algebraic Groups
Introduction to Algebraic Geometry and Algebraic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Algebraic Geometry and Algebraic Groups write by . This book was released on 1980-01-01. Introduction to Algebraic Geometry and Algebraic Groups available in PDF, EPUB and Kindle. Introduction to Algebraic Geometry and Algebraic Groups
Homotopical Algebraic Geometry II: Geometric Stacks and Applications
Homotopical Algebraic Geometry II: Geometric Stacks and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Homotopical Algebraic Geometry II: Geometric Stacks and Applications write by Bertrand Toën. This book was released on 2008. Homotopical Algebraic Geometry II: Geometric Stacks and Applications available in PDF, EPUB and Kindle. 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.
