In preparation (apologies to those who have inquired about the draft of this paper previously announced here under the title "Spectral algebraic theories I: derived categories"; dissatisfaction led to changes in understanding which led to the ongoing rewriting).
January 2026.
Updated July 2026.
Preprint.
With Sanath K. Devalapurkar.
May 2025.
Updated July 2026.
Submitted.
With Jeremy Hahn and Dylan Wilson.
June 2022.
Updated October 2025.
To appear in Annals of Mathematics.
July 2020.
Updated January 2026.
Published in Selecta Mathematica 32 (2026).
With Marc Levine.
August 2018.
Updated February 2020.
Published in Algebra & Number Theory 14.7 (2020).