Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups - 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 Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups write by John Rognes. This book was released on 2008. Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups available in PDF, EPUB and Kindle. 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
Galois Extensions of Structured Ring Spectra - 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 Galois Extensions of Structured Ring Spectra write by John Rognes. This book was released on 2014-09-11. Galois Extensions of Structured Ring Spectra available in PDF, EPUB and Kindle. 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.
Geometric and Topological Aspects of the Representation Theory of Finite Groups
Geometric and Topological Aspects of the Representation Theory of Finite Groups - 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 Geometric and Topological Aspects of the Representation Theory of Finite Groups write by Jon F. Carlson. This book was released on 2018-10-04. Geometric and Topological Aspects of the Representation Theory of Finite Groups available in PDF, EPUB and Kindle. These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
Triangulated Categories in Representation Theory and Beyond
Triangulated Categories in Representation Theory and Beyond - 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 Triangulated Categories in Representation Theory and Beyond write by Petter Andreas Bergh. This book was released on . Triangulated Categories in Representation Theory and Beyond available in PDF, EPUB and Kindle.
Handbook of Homotopy Theory
Handbook of 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 Handbook of Homotopy Theory write by Haynes Miller. This book was released on 2020-01-23. Handbook of Homotopy Theory available in PDF, EPUB and Kindle. The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
