Galois Descent for Real Spectra

Banerjee, Romie

doi:10.48550/arxiv.1305.4360

Cited by 2 publications

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“…and in particular tensoring with A commutes with all limits in C. Since tensoring with A is conservative, we find that the hypotheses of the Barr-Beck-Lurie theorem go into effect (cf. also [Ban13,2.6]). In particular, CB • (A) converges to 1 and, moreover, for any M ∈ C, CB • (A) ⊗ M converges to M .…”

Section: 5mentioning

confidence: 98%

The Galois group of a stable homotopy theory

Mathew

2016

Advances in Mathematics

102

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To a "stable homotopy theory" (a presentable, symmetric monoidal stable ∞-category), we naturally associate a category of finiteétale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call the Galois group. We then calculate the Galois groups in several examples. For instance, we show that the Galois group of the periodic E∞-algebra of topological modular forms is trivial and that the Galois group of K(n)-local stable homotopy theory is an extended version of the Morava stabilizer group. We also describe the Galois group of the stable module category of a finite group. A fundamental idea throughout is the purely categorical notion of a "descendable" algebra object and an associated analog of faithfully flat descent in this context.

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Section: 5mentioning

confidence: 98%

The Galois group of a stable homotopy theory

Mathew

2016

Advances in Mathematics

102

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“…The following result has been observed independently by many authors. Compare in particular [GL,Hes09,Mei12,Ban13].…”

Section: Galois Extensionsmentioning

confidence: 99%

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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Galois Descent for Real Spectra

Cited by 2 publications

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The Galois group of a stable homotopy theory

The Galois group of a stable homotopy theory

Examples of Descent up to Nilpotence

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