Study in derived algebraic geometry : volume I: correspondences and duality - Gaitsgory, Dennis; Rozenblyum, Nick (Providence : American Mathematical Society, 2017)
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.
volume 1. Correspondences and duality.
Includes bibliographical references and index.
Keywords: Algebraic geometry; Duality theory (Mathematics); Lie algebras; Geometry