Topological Cyclic Homology and the Fargues-Fontaine Curve

Explore the intricate connections between topological cyclic homology and the Fargues--Fontaine curve in this 48-minute conference talk by Lars Hesselholt from the University of Copenhagen. Delve into the emergence of the Fargues--Fontaine curve through the localization of invariants, including K-theory and topological cyclic homology. Gain insights into the potential analogous appearance of the twistor projective line. This presentation was part of the Conference on Homotopy Theory with Applications to Arithmetic and Geometry held at the Fields Institute from June 27-30, 2022, offering a deep dive into advanced mathematical concepts at the intersection of homotopy theory, arithmetic, and geometry.