Topological cyclic homology and the Fargues–Fontaine curve

Lars Hesselholt

doi:10.1090/pspum/105/10

Topological cyclic homology and the Fargues–Fontaine curve

Lars Hesselholt^*

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

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Abstract

This paper is an elaboration of my lecture at the conference. The purpose is to explain how the Fargues–Fontaine curve and its decomposition into a punctured curve and the formal neighborhood of the puncture naturally appear from various forms of topological cyclic homology and maps between them. I make no claim of originality. My purpose here is to highlight some of the spectacular material contained in the papers of Nikolaus–Scholze [16], Bhatt–Morrow–Scholze [3], and Antieau–Mathew–Morrow–Nikolaus [1] on topological cyclic homology and in the book by Fargues–Fontaine [7] on their revolutionary curve.

Originalsprog	Engelsk
Titel	Cyclic Cohomology at 40 : Achievements and Future Prospects
Antal sider	14
Forlag	American Mathematical Society
Publikationsdato	2023
Sider	197-210
ISBN (Trykt)	9781470469771
DOI	https://doi.org/10.1090/pspum/105/10
Status	Udgivet - 2023
Begivenhed	Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021 - Virtual, Online Varighed: 27 sep. 2021 → 1 okt. 2021

Konference

Konference	Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021
By	Virtual, Online
Periode	27/09/2021 → 01/10/2021

Navn	Proceedings of Symposia in Pure Mathematics
Vol/bind	105
ISSN	0082-0717

Bibliografisk note

Funding Information:
The author was partially supported by the Danish National Research Foundation through the Copenhagen Center for Geometry and Topology (DNRF151) and by JSPS Grant-in-Aid for Scientific Research number 21K03161.

Publisher Copyright:
© 2023 American Mathematical Society.

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Citationsformater

Hesselholt, L 2023, Topological cyclic homology and the Fargues–Fontaine curve. i Cyclic Cohomology at 40: Achievements and Future Prospects. American Mathematical Society, Proceedings of Symposia in Pure Mathematics, bind 105, s. 197-210, Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021, Virtual, Online, 27/09/2021. https://doi.org/10.1090/pspum/105/10

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