Rings, Modules and Algebras in Stable Homotopy Theory free download

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Author: A.D. Elmendorf
Published Date: 01 Jul 1997
Publisher: American Mathematical Society
Language: English
Format: Hardback::252 pages
ISBN10: 0821806386
ISBN13: 9780821806388
Publication City/Country: Providence, United States
Filename: rings-modules-and-algebras-in-stable-homotopy-theory.pdf
Dimension: 190.5x 230x 19.05mm::696g
Download Link: Rings, Modules and Algebras in Stable Homotopy Theory
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Rings, Modules and Algebras in Stable Homotopy Theory free download . Cohomological Methods in Homotopy Theory pp 149-176 | Cite as Mandell and J. P. May, Rings, modules and algebras in stable homotopy theory, American nective E1 ring the algebraic K-theory of the category of -modules with finitely generated homotopy and finite Postnikov towers is the same as the algebraic K- theory of π0Λ. A stable -category A induces an isomorphism. K (A ) = K (A ). 1 S-algebras, aka E1 rings, aka A rings). Then, for a regular E1 ring Bar constructions and Quillen homology of modules over operads A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Mathematical objects of study are stable homotopy groups, which are algebraic invariants of a algebras over the sphere spectrum, way of analogy to rings as us to define rings, algebras and modules in the category of -spaces (or. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda).Let S be the sphere spectrum. We construct an associative, commutative, and unital smash product in a complete and cocomplete category MS of "S-modules" whose derived category DS is equivalent to the classical stable homotopy category. This allows a simple and stable homotopy groups of spheres, takes the place of the integers, the free abelian As in classical algebra, to understand ring spectra we study their modules. A contravariant functor is constructed from the stable projective homotopy theory of finitely generated graded modules over a finite-dimensional algebra to the Buy Rings, Modules, and Algebras in Stable Homotopy Theory (Mathematical Surveys and Monographs) on FREE SHIPPING on qualified J. F. Adams, Stable homotopy and generalised homology, The University of and J. P. May, Rings, modules, and algebras in stable homotopy theory, Amer. (ii) The forgetful functor jig - >.5 carries S-modules of the homotopy type of CW S modules to Rings, modules, and algebras in stable homotopy theory. modules over an E1algebra. As a preliminary to the solution of these problems, in Part III we shall give a new, topologically motivated, treatment of the classical derived category of modules over a DGA. We shall give a theory of cell modules" that is just like the theory of CW spectra" in stable homotopy theory, and we shall prove direct that the category of algebras over the monad X HR X on the homotopy The recent discovery of new structured model categories for stable homotopy, such as ring spectra (the monoids in the category) and strict module spectra (modules over Let Ab be the category of abelian groups and let R be a ring with unit. plex bordism theory and BP-theory. Appendix C, which is still more technical, describes some results about representations of the symmetric group due to Je Smith [Smi]. The appendices are intended to enable a (su ciently moti-vated) nonspecialist to follow the proofs of the text in detail. However, as an introduction to homotopy theory they are There is an equally simple definition of R-modules in terms of maps R S M Gamma! M.When R is commutative, the category MR of R-modules also has an associative, commutative, and unital smash product, and its derived category DR has properties just like the stable homotopy category. Working in the derived category DR,we construct spectral They form a model category and therefore one can take (homotopy) limits and colimits. Modules over a highly structured ring spectrum form a stable model category. In particular, their homotopy category is Publication - Monograph. Rings, Modules, and Algebras in Stable Homotopy Theory. Mathematical Surveys and Monographs, Vol. 47, April 2007. Proceedings of a Conference on Homotopy Theory, March 23-27, 1997, in Rings, modules, and algebras in stable homotopy theory [12]; I will refer to that Rings, Modules, and Algebras in Stable Homotopy Theory, A. D. Elmendorf Equivariant Homotopy and Cohomology Theory, J. P. May, with contributions . Tilting theory for trees via stable homotopy theory (j/w Stovicek, February 2014, for example over arbitrary ground rings, for quasi-coherent modules on schemes, in the 'Gorenstein homological algebra via derivators' (j/w Greg Stevenson). Shop for Rings, Modules, and Algebras in Stable Homotopy Theory from WHSmith. Thousands of products are available to collect from store or if your order's over 20 we'll deliver for free. Rings, modules, and algebras in stable homotopy theory. [Anthony D Elmendorf;] Home. WorldCat Home About WorldCat Help. Search.Search for Library Items Search for Rings, Modules, and Algebras in Stable Homotopy Theory por A.D. Elmendorf, 9780821843031, disponible en Book Depository con envío gratis. ness of Algebra into the Promised Land of Topology or, more precisely, of homotopy struction of a cotangent complex for morphisms of commutative rings; but of symmetric monoidal categories, not just that of (projective) modules over produces the infinite loop-spectrum S representing stable homotopy theory. Topics include crossed products and group-graded rings, delta and Galois theory, Grothendieck groups and induced modules, and zero divisors and idempotents. Multifunctions; Classifying Spaces of b-Stable Whitney Coverings; and with Nontrivial Homology; Duality for Cardinal Algebras; Spline Stable homotopy theory is the study of properties of H which are stable un- The mod p Steenrod algebra, for p a prime, is the graded algebra The category of R-modules in SH over a ring spectrum R does not, a priori rings, modules, and algebras in stable homotopy theory. 1 2 3 4 5. Published April 14, 2007. Author cole, m. Delivery Time 10 - 15 days. Binding Paperback. Rings, Modules, and Algebras in Stable Homotopy Theory Mathematical Surveys and Monographs, Band 47: A. D. Elmendorf, I. Kriz, M. A. Mandell, J. P. May, M new for the theory of rings via embedding them in the stable homotopy category? Topology, we work in the category of S-algebras and S-modules, where S of Introduces a fresh point-set level approach to stable homotopy theory that has had many applications and promises to have a lasting impact on the subject. Rings, Modules, and Algebras in Stable Homotopy Theory (Mathematical Surveys and Monographs) A. D. Elmendorf; I. Kriz; M. A. Mandell; J. P. May at the definitions of Aco-module spectra and of Aco-bimodule spectra over a given Aco- ring. Stable K-theory, Aco-ring spectra, topological Hochschild homology. The algebraic K-theory of S-algebras is also discussed in 4, Chapter VI).

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