Rings, modules, and algebras in stable homotopy theory
A. D. Elmendorf, I. Kriz, M. A. Mandell, J. P. May, and M. Cole
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
श्रेणियाँ:
साल:
1997
प्रकाशन:
American Mathematical Society
भाषा:
english
पृष्ठ:
265
ISBN 10:
0821806386
ISBN 13:
9780821806388
श्रृंखला:
Mathematical Surveys and Monographs 047
फ़ाइल:
DJVU, 2.72 MB
IPFS:
,
english, 1997