Rings, Modules, and Algebras in Stable Homotopy Theory - Brossura

Elmendorf, A. D.; Kriz, I.; Mandell, M. A.; May, J. P.

Brossura

ISBN 10: 0821843036 ISBN 13: 9780821843031

Casa editrice: Amer Mathematical Society, 2007

Riassunto

This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ""$S$-modules"" whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ""$S$-algebras"" and ""commutative $S$-algebras"" in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0821843036
• ISBN 13: 9780821843031
• Rilegatura: Copertina flessibile
• Numero di pagine: 249
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile