Galois Extensions Of Structured Ring Spectra Stably Dualizable Groups
Download Galois Extensions Of Structured Ring Spectra Stably Dualizable Groups full books in PDF, epub, and Kindle. Read online free Galois Extensions Of Structured Ring Spectra Stably Dualizable Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups
Author | : John Rognes |
Publisher | : American Mathematical Soc. |
Total Pages | : 154 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821840762 |
Download Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups Book 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/Stably Dualizable Groups Related Books
Pages: 154
Pages: 137
Pages: 493
Pages: 275
Pages: 1043