Galois descent for real spectra

Banerjee, Romie

doi:10.1007/s40062-016-0127-1

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…The following result has been observed independently by many authors. Compare in particular [GL,Hes09,Mei12,Ban13]. This result can also be proved for G-Galois extensions when G is not necessarily finite (which we do not discuss here).…”

Section: Examples Of Nilpotencementioning

confidence: 78%

Examples of Descent up to Nilpotence

Mathew

2018

Springer Proceedings in Mathematics &Amp; Statistics

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We give a survey of the ideas of descent and nilpotence. We focus on examples arising from chromatic homotopy theory and from group actions, as well as a few examples in algebra.Date: January 9, 2017.2. Thick ⊗-ideals and nilpotence 2.1. Thick subcategories and ⊗-ideals. We begin by reviewing the theory of thick subcategories. As this material is very classical, we will be brief.Let C be an idempotent-complete stable ∞-category.

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Section: Examples Of Nilpotencementioning

confidence: 78%

Examples of Descent up to Nilpotence

Mathew

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Descent and cyclotomic redshift for chromatically localized algebraic 𝐾-theory

Ben-Moshe,

Carmeli,

Schlank

et al. 2024

J. Amer. Math. Soc.

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We prove that T ( n + 1 ) T(n+1) -localized algebraic K K -theory satisfies descent for π \pi -finite p p -group actions on stable ∞ \infty -categories of chromatic height up to n n , extending a result of Clausen–Mathew–Naumann–Noel for finite p p -groups. Using this, we show that it sends T ( n ) T(n) -local Galois extensions to T ( n + 1 ) T(n+1) -local Galois extensions. Furthermore, we show that it sends cyclotomic extensions of height n n to cyclotomic extensions of height n + 1 n+1 , extending a result of Bhatt–Clausen–Mathew for n = 0 n=0 . As a consequence, we deduce that K ( n + 1 ) K(n+1) -localized K K -theory satisfies hyperdescent along the cyclotomic tower of any T ( n ) T(n) -local ring. Counterexamples to such cyclotomic hyperdescent for T ( n + 1 ) T(n+1) -localized K K -theory were constructed by Burklund, Hahn, Levy and the third author, thereby disproving the telescope conjecture.

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THH and base-change for Galois extensions of ring spectra

Mathew

2017

Algebr. Geom. Topol.

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We treat the question of base-change in T HH for faithful Galois extensions of ring spectra in the sense of Rognes. Given a faithful Galois extension A → B of ring spectra, we consider whether the map T HH(A) ⊗ A B → T HH(B) is an equivalence. We reprove and extend positive results of Weibel-Geller and McCarthy-Minasian and offer new examples of Galois extensions for which base-change holds. We also provide a counterexample where base-change fails.

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Galois descent for real spectra

Cited by 3 publications

References 12 publications

Examples of Descent up to Nilpotence

Examples of Descent up to Nilpotence

Descent and cyclotomic redshift for chromatically localized algebraic 𝐾-theory

THH and base-change for Galois extensions of ring spectra

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