## A Third Isomorphism Theorem for Thom Spectra and Hopf-Galois Extensions

### Jonathan Beardsley – 22 March 2017

I'll describe a method of taking iterated quotients of ring spectra (or any E_n-monoid in a stable, presentable infinity category) by actions of E_n-monoidal Kan complexes and show (roughly) that in the presence of a fibration of E_n-monoidal Kan complexes one can take recognizable intermediate quotients. I will also explain how this relates to Hopf-Galois extensions, which are non-commutative geometric analogues of principal G-bundles, and Koszul duality.

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