{"product_id":"9781470452841-a-study-in-derived-algebraic-geomet","title":"A Study in Derived Algebraic Geometry","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eVolume I: Correspondences and Duality\u003cbr\u003eDerived 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.\u003cbr\u003eDerived 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.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":55110067061110,"sku":"9781470452841","price":127.35,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_37701033.jpg?v=1773961691","url":"https:\/\/www.rarewaves.com\/products\/9781470452841-a-study-in-derived-algebraic-geomet","provider":"Rarewaves.com","version":"1.0","type":"link"}