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p-adic K-theory and topological cyclic homology

[Moved Online] (∞, n)-categories, factorization homology, and algebraic K-theory March 23, 2020 - March 27, 2020

March 24, 2020 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Akhil Mathew (University of Chicago)
Location: MSRI: Online/Virtual
  • algebraic K-theory

  • topological cyclic homology

  • cyclotomic trace

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification



The cyclotomic trace from algebraic K-theory to topological cyclic homology is an important computational tool because of the Dundas-Goodwillie-McCarthy theorem, which states that the trace induces an isomorphism of relative theories with respect to nilpotent ideals. After p-adic completion, this result can be strengthened to henselian pairs, generalizing also the Gabber-Suslin rigidity theorem in the l-adic context. I will explain this generalization and some consequences. Joint with Dustin Clausen and Matthew Morrow.

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