Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups
By John Rognes. 2008
153 citations recorded by the source corpus.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5d139ec36792e0af11ae1a8c76f3bcc3e8435b5b
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In Mathematical Physics
Citations in the corpus
- The C2–spectrum Tmf1(3) and its invertible modules (2015, background): “ic(O X(U\V)) Pic(O X(V)). As noted above, this gluing datum denes an invertible O X-module on Xand this invertible module represents @(g). Let now A!Bbe a faithful G-Galois extension in the sense of [Rog08]. Then by [MS14, Section 3.3], we have the following theorem: Theorem 6.4. There is an equival”
- Hyperdescent and étale K-theory (2019, methodology): “note p-localization together with the finite localization away from a type (n+1) (p-local) finite spectrum. 9In particular, we do not consider here the more general Galois extensions of ring spectra of [Rog08]. 59 Proposition 5.24. Let A be a connective E2-algebra. Then the functor B →L f n(K≥0(B)) de”
- Derived algebraic geometry (2014, background): “It has also been pushed further with the introduction of the new idea that ring spectra should also have an interesting Galois theory (see [106, 114, 93]), leading to the feeling that there should exists an étale topology for ring spectra that extends the usual étale topology for schemes.”
- Derived Algebraic Geometry (2014, background): “It has also been pushed further with the introduction of the new idea that ring spectra should also have an interesting Galois theory (see [106, 114, 93]), leading to the feeling that there should exists an étale topology for ring spectra that extends the usual étale topology for schemes.”
- Affineness and chromatic homotopy theory (2013, methodology): “Rognes’s notion of a faithful Galois extension (Definition 5.1) is a generalization of the above notion of étaleness (or at least the Galois version) that encompasses examples such as KO → KU .”
- Nilpotence and descent in equivariant stable homotopy theory (2015, methodology): “Σ−2CP2 ≃KUG. Here CP2 is considered as a pointed space with trivial G-action. We then develop an analogous Z/2-Galois descent picture from equivariant complex to real K-theory (which is due to Rognes [Rog08] for G= 1). In particular, we show that (for any compact Lie group G) the map KO G→KUG of E∞-”
- The Galois group of a stable homotopy theory (2014, methodology): “of the Galois group and fit into a sequence (19) πweak 1(C) ։π(C) ։πet 1 SpecR0. Definition 6.11. We will say that the Galois theory of Cis algebraic if these maps are isomorphisms. It is an insight of [Rog08] that the second map in (19) is generally not an isomorphism: that is, there are examples of ”