A Study in Derived Algebraic Geometry
Volume I: Correspondences and Duality
Seiten
2017
American Mathematical Society (Verlag)
978-1-4704-5284-1 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5284-1 (ISBN)
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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 ?-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.
This 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.
Dennis Gaitsgory, Harvard University, Cambridge, MA. Nick Rozenblyum, University of Chicago, IL.
| Erscheinungsdatum | 01.03.2021 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-5284-7 / 1470452847 |
| ISBN-13 | 978-1-4704-5284-1 / 9781470452841 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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