Stable categories and structured ring spectra
著者
書誌事項
Stable categories and structured ring spectra
（Mathematical Sciences Research Institute publications, 69）
Cambridge University Press, 2022
- : hardback
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注記
Includes bibliographical references (p. [403]-420) and index
内容説明・目次
内容説明
This comprehensive text focuses on the homotopical technology in use at the forefront of modern algebraic topology. Following on from a standard introductory algebraic topology sequence, it will provide students with a comprehensive background in spectra and structured ring spectra. Each chapter is an extended tutorial by a leader in the field, offering the first really accessible treatment of the modern construction of the stable category in terms of both model categories of point-set diagram spectra and infinity-categories. It is one of the only textbook sources for operadic algebras, structured ring spectra, and Bousfield localization, which are now basic techniques in the field, and the book provides a rare expository treatment of spectral algebraic geometry. Together the contributors - Emily Riehl, Daniel Dugger, Clark Barwick, Michael A. Mandell, Birgit Richter, Tyler Lawson, and Charles Rezk - offer a complete, authoritative source to learn the foundations of this vibrant area.
目次
- 1. Introduction Andrew J. Blumberg, Teena Gerhardt, and Michael A. Hill
- 2. Homotopical categories: from model categories to ( ,1)-categories Emily Riehl
- 3. Stable categories and spectra via model categories Daniel Dugger
- 4. Stable homotopy theory via -categories Clark Barwick
- 5. Operads and operadic algebras in homotopy theory Michael A. Mandell
- 6. Commutative ring spectra Birgit Richter
- 7. An introduction to Bousfield localization Tyler Lawson
- 8. Spectral algebraic geometry Charles Rezk
- Bibliography
- Index.
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