Detecting and describing ramification for structured ring spectra

Abstract: This is a report on joint work in progress with Eva Höning.

Ramification for commutative ring spectra can be detected by relative topological Hochschild homology and by the spectrum of Kähler differentials. For rings of integers in an extension of number fields, 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 norm map. We take the latter fact and use the Tate cohomology spectrum to detect wild ramification in the context of commutative ring spectra. In the talk, I will discuss several examples in the context of topological K-theory and modular forms.

algebraic topology

Audience: researchers in the topic

Online algebraic topology seminar

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