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OP-10285Status unassessedNumber theory

Approach to Fargues-Fontaine Curve using THH · Question 7.1

Chromatic homotopy theory and p-adic geometry · AIMPL workshop record

MSC 55 · Algebraic topology

Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

There is an identification THH(Zp)≅t≥0(im(J))tCp\text{THH}(\mathbf{Z}_p) \cong t_{\ge 0} (\text{im}(J))^{tC_p}. Does this isomorphism yield an integral version of the Fargues-Fontaine curve?

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Background

Question context

Analogy coming from period rings and the modulo pp isomorphism THH(Fp)≅t>0(im(J))tCp\text{THH}(\mathbf{F}_p) \cong t_{> 0} (\text{im}(J))^{tC_p}.

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References
  1. [1]Chromatic homotopy theory and p-adic geometry · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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