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Mathew, Akhil
Advances in mathematics (New York. 1965), 03/2016, Letnik: 291Journal Article
To a “stable homotopy theory” (a presentable, symmetric monoidal stable ∞-category), we naturally associate a category of finite étale 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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