[PDF] Detecting And Describing Ramification For Structured Ring Spectra eBook

Author : Andrew Baker
Publisher : Cambridge University Press
Page : 246 pages
File Size : 43,55 MB
Release : 2004-11-18
Category : Mathematics
ISBN : 9780521603058

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This book contains some important new contributions to the theory of structured ring spectra.

Author : John Rognes
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 49,90 MB
Release : 2008
Category : Mathematics
ISBN : 0821840762

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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 $E$.

Author : Douglas C. Ravenel
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 11,93 MB
Release : 2003-11-25
Category : Mathematics
ISBN : 082182967X

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Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.

Author : H.R. Margolis
Publisher : Elsevier
Page : 511 pages
File Size : 21,67 MB
Release : 2011-08-18
Category : Mathematics
ISBN : 0080960170

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I have intended this book to be more than just the sum of its chapters, and the introduction is, in part, an attempt to spell out what the more is. Algebraic topology is the study of topological problems by algebraic means. More precisely, this has come to be framed as the study of topological categories by means of functors to algebraic categories. Beyond the basic definitions and structure, the focus is often on particular problems, for example, Adams’ use of K-theory to solve the vector fields on spheres problem. On the other hand, there are contributions of a more global nature yielding insight into the overall structure of some topological category, for example, Quillen’s work on rational homotopy type. This book is intended primarily as a contribution of this latter sort. So while there will be a variety of particular examples and computations, and although the structure being developed has significant application to many specific problems (some of which are considered here), the major thrust of the text is toward understanding the global structure and linkage of the topological and algebraic categories considered: the stable homotopy category and the category of modules over the Steenrod algebra.

Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 39,8 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387226397

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Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Author : A. I. Scott
Publisher : Elsevier
Page : 458 pages
File Size : 48,30 MB
Release : 2013-10-22
Category : Science
ISBN : 1483137201

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Interpretation of the Ultraviolet Spectra of Natural Products focuses on the ultraviolet spectrum of chromophores. The book first discusses single chromophores, including absorption due to electron lone pairs in saturated systems and absorption of olefins, alkynes, carbonyl compounds, and thiocarbonyl compounds. The text also takes a look at conjugated chromosomes, such as polyenes, enynes, and conjugated azomethines. The selection also evaluates C-aromatic compounds. Topics include benzenoid and hydrocarbons; phenols and their ethers; styrenes and stilbenes; aromatic carbonyl compounds; and nitro compounds. The text also discusses O- and S- heteroaromatic compounds and N-heteroaromatic compounds. The book highlights the applications of spectrophotometry to the analysis of natural products. Topics include formation of derivatives having absorbing chromophores; reactions leading to changes in absorption of added reagents; and analyses involving transformation to products suitable for spectrophotometry. The text is a good reference for readers wanting to explore chromophores.

Author : David Eisenbud
Publisher : Cambridge University Press
Page : 633 pages
File Size : 20,85 MB
Release : 2016-04-14
Category : Mathematics
ISBN : 1107017084

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3264, the mathematical solution to a question concerning geometric figures.