Galois Extensions of Structured Ring Spectra Stably Dualizable Groups is popular PDF and ePub book, written by John Rognes in 2008, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Galois Extensions of Structured Ring Spectra Stably Dualizable Groups can be Read Online from any device for your convenience.
Galois Extensions of Structured Ring Spectra Stably Dualizable Groups Book PDF Summary
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 $E$.
Detail Book of Galois Extensions of Structured Ring Spectra Stably Dualizable Groups PDF
- Author : John Rognes
- Release : 29 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821840764
- Genre : Mathematics
- Total Page : 154 pages
- Language : English
- PDF File Size : 18,8 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Galois Extensions of Structured Ring Spectra Stably Dualizable Groups by John Rognes, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.