Geodesic
Detecting and describing ramification for structured ring spectra
Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 529-554

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DOI

John Rognes developed a notion of Galois extension of commutative ring spectra, and this includes a criterion for identifying an extension as unramified. Ramification for commutative ring spectra can be detected by relative topological Hochschild homology and by topological André–Quillen homology. In the classical algebraic context, it is important to distinguish between tame and wild ramification. Noether’s theorem characterizes tame ramification in terms of a normal basis, and tame ramification can also be detected via the surjectivity of the trace map. For commutative ring spectra, we suggest to study the Tate construction as a suitable analog. It tells us at which integral primes there is tame or wild ramification, and we determine its homotopy type in examples in the context of topological K-theory and topological modular forms.
DOI : 10.1017/S0017089523000083
Mots-clés : Tame ramification, wild ramification, topological André–Quillen homology, topological Hochschild homology, topological modular forms, Tate vanishing 
Höning, Eva; Richter, Birgit. Detecting and describing ramification for structured ring spectra. Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 529-554. doi: 10.1017/S0017089523000083
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