Mathematical Sciences Research Institute

Home » Workshop » Schedules » Excision and algebraic K-theory

Excision and algebraic K-theory

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

March 23, 2020 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Markus Land (University of Copenhagen)
Location: MSRI: Online/Virtual
  • algebraic K-theory

  • higher algebra

  • chromatic homotopy theory

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification



I will report on joint work with Tamme. I will recall that algebraic K-theory does not satisfy excision and describe an effective way of studying the failure for excision in any localizing invariant. As applications we find a short proof of Suslin's excision theorem, that what we call truncating invariants satisfy excision, and new ways of calculating algebraic K-groups of certain rings. Examples of truncating invariants include periodic cyclic homology over the rationals and the fibre of the cyclotomic trace. If time permits I will also indicate joint work with Tamme and Meier, where we study chromatic localizations of algebraic K-theory. As applications of our approach we show that K(1)-localized algebraic K-theory satisfies excision (first proven by Bhatt--Clausen--Mathew) and that the K(n)-localized K-theory of any bounded above connective ring spectrum vanishes for n at least 2.

Supplements No Notes/Supplements Uploaded
Video/Audio Files


H.264 Video 918_28214_8256_1-Land.mp4
Troubles with video?

Please report video problems to itsupport@msri.org.

See more of our Streaming videos on our main VMath Videos page.