A Study in Derived Algebraic Geometry: Volume I: Correspondences and Duality (Mathematical Surveys and Monographs) - Tapa blanda

Gaitsgory, Dennis; Rozenblyum, Nick

 
9781470452841: A Study in Derived Algebraic Geometry: Volume I: Correspondences and Duality (Mathematical Surveys and Monographs)
Tapa blanda
ISBN 10: 1470452847 ISBN 13: 9781470452841
Editorial: American Mathematical Society, 2017

Sinopsis

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.

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Acerca del autor

Dennis Gaitsgory, Harvard University, Cambridge, MA.

Nick Rozenblyum, University of Chicago, IL.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
American Mathematical Society
Año de publicación
2017
Idioma
Inglés
ISBN 10 
1470452847
ISBN 13 
9781470452841
Encuadernación
Tapa blanda
Número de páginas
533
Contacto del fabricante
no disponible
Persona responsable
no disponible