A Study in Derived Algebraic Geometry: Correspondences and Duality (Mathematical Surveys and Monographs)

Dennis Gaitsgory

Published by American Mathematical Society, 2017
ISBN 10: 1470435691 / ISBN 13: 9781470435691
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Synopsis: 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.

About the Author: Dennis Gaitsgory, Harvard University, Cambridge, MA.Nick Rozenblyum, University of Chicago, IL.

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Title: A Study in Derived Algebraic Geometry: ...
Publisher: American Mathematical Society
Publication Date: 2017
Binding: Hardcover
Book Condition: New

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