Axiomatic Stable Homotopy Theory

Axiomatic Stable Homotopy Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 130
Release :
ISBN-10 : 9780821806241
ISBN-13 : 0821806246
Rating : 4/5 (41 Downloads)

Book Synopsis Axiomatic Stable Homotopy Theory by : Mark Hovey

Download or read book Axiomatic Stable Homotopy Theory written by Mark Hovey and published by American Mathematical Soc.. This book was released on 1997 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define and investigate a class of categories with formal properties similar to those of the homotopy category of spectra. This class includes suitable versions of the derived category of modules over a commutative ring, or of comodules over a commutative Hopf algebra, and is closed under Bousfield localization. We study various notions of smallness, questions about representability of (co)homology functors, and various kinds of localization. We prove theorems analogous to those of Hopkins and Smith about detection of nilpotence and classification of thick subcategories. We define the class of Noetherian stable homotopy categories, and investigate their special properties. Finally, we prove that a number of categories occurring in nature (including those mentioned above) satisfy our axioms.


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