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Descent in algebraic K-theory via May's nilpotence conjecture

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Akhil Mathew
University of California at Berkeley
Die, 16/06/2015 - 15:00 - 16:00
MPIM Lecture Hall
A general Galois descent question in algebraic K-theory asks when the K-theory of stable infinity-categories commutes (after some localization) with homotopy fixed points for finite group actions. In joint work with Niko Naumann and Justin Noel, we approach this question using "derived induction and restriction theory" in the category of equivariant spectra. A key ingredient is a (proved) conjecture of J.P. May which states that the nilpotence of elements in H-infinity-ring spectra can be detected using integral homology. This yields an efficient tool for proving that E-infinity-algebras in G-spectra are nilpotent with respect to a family of subgroups. When applied to equivariant versions of algebraic K-theory, we prove various descent results in algebraic K-theory as well as an analog of Mitchell's theorem for K(KU) at p = 2, 3
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