Study in Derived Algebraic Geometry (eBook)

Dennis Gaitsgory (Autor)

eBook Download: PDF

2017
533 Seiten
American Mathematical Society (Verlag)
978-1-4704-4085-5 (ISBN)

Infos

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 "e;renormalization"e; 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 $/infty$-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 $/mathrm{(}/infty, 2/mathrm{)}$-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 $/mathrm{(}/infty, 2/mathrm{)}$-categories needed for the third part.

Produkt-Details

• Erscheint lt. Verlag: 7.6.2017
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-4085-7 / 1470440857
• ISBN-13: 978-1-4704-4085-5 / 9781470440855