Reading course on topological Hochschild homology

The purpose of this course is to give an introduction to topological Hochschild homology and p-adic Hodge theory.

Time: Tuesdays 4:00 p.m. - 6:00 p.m.
Place: Auditorium 7 or 10, the latter marked with an asterisque.
Course administrator: Esben Auseth Nielsen.


November 17: Introduction (Lars Hesselholt)
November 24: Witt vectors (Amalie Høgenhaven)
December 1: Cyclotomic spectra (Rune Haugseng)
December 8: Topological Hochschild homology (Irakli Patchkoria)
December 15: Topological Hochschild homology of finite fields (Guozhen Wang)
January 12: The de Rham-Witt complex (Dan Petersen)
January 20: Topological Hochschild homology of perfectoid fields (Lars Hesselholt)*
January 27: Scholze's filtration of topological Hochschild homology (Gijs Heuts)*


  • J. Borger, The basic geometry of Witt vectors, I: The affine case, Algebra Number Theory 2 (2011), 231-285.
  • L. Hesselholt, On the topological cyclic homology of the algebraic closure of a local field, An Alpine Anthology of Homotopy Theory: Proceedings of the Second Arolla Conference on Algebraic Topology (Arolla, Switzerland, 2004), pp. 133-162, Contemp. Math. 399, Amer. Math. Soc., Providence, RI, 2006.
  • L. Hesselholt, The big de Rham-Witt complex, Acta Math. 214 (2015), 135-207.
  • L. Hesselholt, I. Madsen, On the K-theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997), 29-102.
  • L. Illusie, Complexe de de Rham-Witt et cohomologie cristalline, Ann. Sci. École Norm. Sup. 12 (1979), 501-661.
  • J. Lurie, Higher algebra, in preparation.