## 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.

**Schedule**:

November 17: Introduction (Lars Hesselholt)

November 24: Witt vectors (Amalie HÃ¸genhaven)

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)*

**Literature**:

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.