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.
Homotopical Algebraic Geometry II
Homotopical Algebraic Geometry II - 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 write by Bertrand Toën. This book was released on 2014-09-11. Homotopical Algebraic Geometry II available in PDF, EPUB and Kindle. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category. 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.
Algebraic Geometry over C∞-Rings
Algebraic Geometry over C∞-Rings - 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 Geometry over C∞-Rings write by Dominic Joyce. This book was released on 2019-09-05. Algebraic Geometry over C∞-Rings available in PDF, EPUB and Kindle. If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.
Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects
Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects - 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 Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects write by Frank Neumann. This book was released on 2021-09-29. Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects available in PDF, EPUB and Kindle. This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.
Simplicial Methods for Operads and Algebraic Geometry
Simplicial Methods for Operads and Algebraic Geometry - 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 Simplicial Methods for Operads and Algebraic Geometry write by Ieke Moerdijk. This book was released on 2010-12-01. Simplicial Methods for Operads and Algebraic Geometry available in PDF, EPUB and Kindle. "This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"--Foreword
