Dustin Clausen : Algebraic K-theory and Chromatic Homotopy Theory

Collection Dustin Clausen : Algebraic K-theory and Chromatic Homotopy Theory

Organisateur(s)
Date(s) 18/02/2025 - 27/02/2025
00:00:00 / 00:00:00
4 4

Algebraic K-theory and Chromatic Homotopy Theory (4/4)

De Dustin Clausen

The most universal kind of linear algebra is based not on abelian groups, but on homotopy-theoretic objects known as spectra. According to chromatic homotopy theory, one can systematically organize spectra into periodic families.  On the other hand, a natural source of spectra is provided by algebraic K-theory, a highly refined cohomological invariant of rings (or schemes, etc).  This leads to the subject of this course: the interaction of the chromatic theory with algebraic K-theory.  The story begins with classical theorems of Thomason, Mitchell, and Hesselholt-Madsen.  Bold generalizations of these theorems were conjectured by Rognes and Ausoni-Rognes, under the umbrella term of "redshift".  Several of these conjectures are now theorems due to recent work of many people.  Remarkably, this work has applications to "pure" chromatic homotopy theory: Burklund-Hahn-Levy-Schlank used it to settle (in the negative) the "telescope conjecture", the last of Ravenel's conjectures.   Lecture 1: Introduction to chromatic homotopy theory.

Lecture 2: Descent and "soft redshift".

Lecture 3: "Hard redshift", a.k.a. the Lichtenbaum-Quillen property.

Lecture 4: The telescope conjecture.

Informations sur la vidéo

  • Date de captation 27/02/2025
  • Date de publication 27/02/2025
  • Institut IHES
  • Langue Anglais
  • Audience Chercheurs, Doctorants
  • Format MP4

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