Axiomatic Stable Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Axiomatic Stable Homotopy Theory write by Mark Hovey. This book was released on 1997. Axiomatic Stable Homotopy Theory available in PDF, EPUB and Kindle. 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.
Axiomatic Stable Homotopy Theory Paperback
Axiomatic Stable Homotopy Theory Paperback - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Axiomatic Stable Homotopy Theory Paperback write by Mark Hovey. This book was released on 2014-09-11. Axiomatic Stable Homotopy Theory Paperback available in PDF, EPUB and Kindle. This work gives an axiomatic presentation of stable homotopy theory. It starts with axioms defining a stable homotopy category; using these axioms, one can make various constructions - cellular towers, Bousfield localization, and Brown representability, to name a few. Much of the book is devoted to these constructions and to the study of the global structure of stable homotopy categories.
Axiomatic, Enriched and Motivic Homotopy Theory
Axiomatic, Enriched and Motivic Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Axiomatic, Enriched and Motivic Homotopy Theory write by John Greenlees. This book was released on 2012-12-06. Axiomatic, Enriched and Motivic Homotopy Theory available in PDF, EPUB and Kindle. The NATO Advanced Study Institute "Axiomatic, enriched and rna tivic homotopy theory" took place at the Isaac Newton Institute of Mathematical Sciences, Cambridge, England during 9-20 September 2002. The Directors were J.P.C.Greenlees and I.Zhukov; the other or ganizers were P.G.Goerss, F.Morel, J.F.Jardine and V.P.Snaith. The title describes the content well, and both the event and the contents of the present volume reflect recent remarkable successes in model categor ies, structured ring spectra and homotopy theory of algebraic geometry. The ASI took the form of a series of 15 minicourses and a few extra lectures, and was designed to provide background, and to bring the par ticipants up to date with developments. The present volume is based on a number of the lectures given during the workshop. The ASI was the opening workshop of the four month programme "New Contexts for Stable Homotopy Theory" which explored several themes in greater depth. I am grateful to the Isaac Newton Institute for providing such an ideal venue, the NATO Science Committee for their funding, and to all the speakers at the conference, whether or not they were able to contribute to the present volume. All contributions were refereed, and I thank the authors and referees for their efforts to fit in with the tight schedule. Finally, I would like to thank my coorganizers and all the staff at the Institute for making the ASI run so smoothly. J.P.C.GREENLEES.
Memoirs of the American Mathematical Society
Memoirs of the American Mathematical Society - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Memoirs of the American Mathematical Society write by . This book was released on 1988. Memoirs of the American Mathematical Society available in PDF, EPUB and Kindle.
Nilpotence and Periodicity in Stable Homotopy Theory
Nilpotence and Periodicity in Stable Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nilpotence and Periodicity in Stable Homotopy Theory write by Douglas C. Ravenel. This book was released on 1992-11-08. Nilpotence and Periodicity in Stable Homotopy Theory available in PDF, EPUB and Kindle. Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
