Katzarkov–Kontsevich–Pantev conjecture
For every smooth and proper differential -graded category over , the Getzler–Gauss–Manin connection in the -direction on the periodic cyclic homology has a regular singularity at and quasi-unipotent monodromy.
References
Primary source
Additional references
- p-curvature in non-commutative Hodge theory and the Kontsevich-Soibelman operad — arXiv — Zihong Chen
Progress summary
A newly posted paper claims to prove the conjecture, but the result has not been independently checked.
The Katzarkov–Kontsevich–Pantev conjecture links noncommutative Hodge theory with geometric properties of Landau–Ginzburg models. The retrieved literature records substantial special cases, but not a general proof before the latest claim.
Known results
- Smooth Fano threefolds, including higher Picard-rank cases (Cheltsov and Przyjalkowski, 2018).
- Minimal semisimple adjoint orbits viewed as Landau–Ginzburg models (2023 version).
- Some additional SLFs, while the conjecture remains unknown for all SLFs (2025).
September 2026 claimed proof
On September 22, 2026, Zihong Chen's paper proposed a reduction-mod- proof using multiplicative -curvature and the Kontsevich–Soibelman operad. If correct, this would settle the full conjecture; the claim is unverified.
Current status (as of September 2026): A full proof is claimed by Zihong Chen but remains unverified; only special cases are established in the retrieved literature.
Solutions 0
No solutions have been posted yet.