Structured Ring Spectra
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Structured Ring Spectra
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Author : Andrew Baker
language : en
Publisher: Cambridge University Press
Release Date : 2004-11-18
Structured Ring Spectra written by Andrew Baker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-18 with Mathematics categories.
This book contains some important new contributions to the theory of structured ring spectra.
Stable Categories And Structured Ring Spectra
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Author : Andrew J. Blumberg
language : en
Publisher: Cambridge University Press
Release Date : 2022-07-21
Stable Categories And Structured Ring Spectra written by Andrew J. Blumberg and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-21 with Mathematics categories.
A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.
Galois Extensions Of Structured Ring Spectra Stably Dualizable Groups
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Author : John Rognes
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Galois Extensions Of Structured Ring Spectra Stably Dualizable Groups written by John Rognes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The author introduces the notion of a Galois extension of commutative $S$-algebras ($E_\infty$ ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, real and complex topological $K$-theory, Lubin-Tate spectra and cochain $S$-algebras. He establishes the main theorem of Galois theory in this generality. Its proof involves the notions of separable and etale extensions of commutative $S$-algebras, and the Goerss-Hopkins-Miller theory for $E_\infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions. The author extends the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein and the $p$-complete study for $p$-compact groups by T. Bauer, to a general duality theory for stably dualizable groups in the $E$-local stable homotopy category, for any spectrum $E$.
Galois Extensions Of Structured Ring Spectra
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Author : John Rognes
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11
Galois Extensions Of Structured Ring Spectra written by John Rognes and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Commutative algebra categories.
Galois Extensions of Structured Ring Spectra: Abstract Introduction Galois extensions in algebra Closed categories of structured module spectra Galois extensions in topology Examples of Galois extensions Dualizability and alternate characterizations Galois theory I Pro-Galois extensions and the Amitsur complex Separable and etale extensions Mapping spaces of commutative $S$-algebras Galois theory II Hopf-Galois extensions in topology References Stably Dualizable Groups: Abstract Introduction The dualizing spectrum Duality theory Computations Norm and transfer maps References Index.
H Ring Spectra And Their Applications
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Author : Robert R. Bruner
language : en
Publisher: Springer
Release Date : 2006-11-14
H Ring Spectra And Their Applications written by Robert R. Bruner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
E Infinite Ring Spaces And E Infinite Ring Spectra
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Author : J.P. May
language : en
Publisher: Springer
Release Date : 2006-11-14
E Infinite Ring Spaces And E Infinite Ring Spectra written by J.P. May and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Rings Modules And Algebras In Stable Homotopy Theory
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Author : Anthony D. Elmendorf
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Rings Modules And Algebras In Stable Homotopy Theory written by Anthony D. Elmendorf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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
H Ring Spectra And Their Applications
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Author : Robert R. Bruner
language : en
Publisher:
Release Date : 2014-01-15
H Ring Spectra And Their Applications written by Robert R. Bruner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Equivariant Orthogonal Spectra And S Modules
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Author : M. A. Mandell
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Equivariant Orthogonal Spectra And S Modules written by M. A. Mandell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The last few years have seen a revolution in our understanding of the foundations of stable homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy categories are equivalent to the stable homotopy category are now known, whereas no such categories were known before 1993. The most well-known examples are the category of $S$-modules and the category of symmetric spectra. We focus on the category of orthogonal spectra, which enjoys some of the best features of $S$-modules and symmetric spectra and which is particularly well-suited to equivariant generalization. We first complete the nonequivariant theory by comparing orthogonal spectra to $S$-modules. We then develop the equivariant theory.For a compact Lie group $G$, we construct a symmetric monoidal model category of orthogonal $G$-spectra whose homotopy category is equivalent to the classical stable homotopy category of $G$-spectra. We also complete the theory of $S_G$-modules and compare the categories of orthogonal $G$-spectra and $S_G$-modules. A key feature is the analysis of change of universe, change of group, fixed point, and orbit functors in these two highly structured categories for the study of equivariant stable homotopy theory.
Spaces Of Orderings And Abstract Real Spectra
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Author : Murray A. Marshall
language : en
Publisher: Springer
Release Date : 2006-11-17
Spaces Of Orderings And Abstract Real Spectra written by Murray A. Marshall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-17 with Mathematics categories.
This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.