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SUMMARY:Morava K-theory of Algebraic K-theory and Topological Periodic Cyc
 lic Homology
DTSTART:20200421T101500
DTEND:20200421T111500
DTSTAMP:20260916T194621Z
UID:8767d3e0d63c7312c9ccc1653ec67e5bbdd1aff9a3352a318541f82e
CATEGORIES:Conferences - Seminars
DESCRIPTION:Gabriel Angelini-Knoll\, Freie Universität Berlin\nThe chrom
 atic red-shift program of Ausoni-Rognes suggests that algebraic K-theory s
 hifts chromatic height by one. In my talk\, I will describe a computationa
 l approach to this program where chromatic height is measured by vanishing
  of Morava K-theory. In particular\, we see that the vanishing range of Mo
 rava K-theory of topological periodic cyclic homology of a certain family 
 of Thom spectra y(n) increases by one. We also prove that algebraic K-theo
 ry preserves vanishing of Morava K-theory for y(n)\, a result recently pro
 ven in parallel by Land-Meier-Tamme by entirely different methods. Our the
 orem relies on a technical result about when commuting Morava K-theory wit
 h a sequential limit is possible\, which I will discuss. As second applica
 tion of this technical result\, we prove a higher chromatic height analogu
 e of Mitchell’s theorem for truncated Brown-Peterson spectra associated 
 to a prime p and an integer n\, which remains conditional for large primes
  p and integers n. This is based on joint work with J.D. Quigley and joint
  work with A. Salch.
LOCATION:The World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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