{"product_id":"a-study-in-derived-algebraic-geometry-volume-i-correspondences-and-duality","title":"Study in Derived Algebraic Geometry","description":"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.\u003cbr\u003e\u003cbr\u003eThis volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of ?-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 (?,2)-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 (?,2)-categories needed for the third part.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":54280661336408,"sku":null,"price":122.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9781470452841_69ecf2da-cc70-4085-871c-20a38b34dce4.jpg?v=1779511562","url":"https:\/\/agendabookshop.com\/products\/a-study-in-derived-algebraic-geometry-volume-i-correspondences-and-duality","provider":"Agenda Bookshop","version":"1.0","type":"link"}