Correspondences and duality

著者

• Gaitsgory, D. (Dennis)
• Rozenblyum, Nick

書誌事項

Correspondences and duality

Dennis Gaitsgory, Nick Rozenblyum

（Mathematical surveys and monographs, v. 221 . A study in derived algebraic geometry ; v. 1）

American Mathematical Society, c2017

注記

Includes bibliographical references (p. 525-526) and indexes

内容説明・目次

内容説明

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 $\infty$-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.

目次

Preliminaries: Introduction Some higher algebra Basics of derived algebraic geometry Quasi-coherent sheaves on prestacks Ind-coherent sheaves: Introduction Ind-coherent sheaves on schemes Ind-coherent sheaves as a functor out of the category of correspondences Interaction of Qcoh and IndCoh Categories of correspondences: Introduction The $(\infty,2)$-category of correspondences Extension theorems for the category of correspondences The (symmetric) monoidal structure on the category of correspondences $(\infty,2)$-categories: Introduction Basics of 2-categories Straightening and Yoneda for $(\infty,2)$-categories Adjunctions in $(\infty,2)$-categories Bibliography Index of notations Index.

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詳細情報

• NII書誌ID(NCID): BB24424829
• ISBN:
  • 9781470435691
• LCCN: 2016054809
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xl, 533 p.
• 大きさ: 27 cm
• 分類:
  • DC23 : 516.35
• 件名:
  • LCSH : Geometry, Algebraic
  • LCSH : Duality theory (Mathematics)
  • LCSH : Lie algebras
  • LCSH : Geometry
• 親書誌ID:
  • BA00134419