# p-adic K-theory and topological cyclic homology

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

**Speaker(s):**Akhil Mathew (University of Chicago)

**Location:**SLMath: Online/Virtual

**Tags/Keywords**

algebraic K-theory

topological cyclic homology

cyclotomic trace

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**

#### 4-Mathew

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.

#### 4-Mathew

H.264 Video | 918_28215_8259_4-Mathew.mp4 |

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