A non-abelian p-curvature result in algebraic geometry
burny_tech · x · 2026-07-20
A new paper by Yeuk Hay Joshua Lam and Daniel Litt extends Katz’s p-curvature conjecture to a non-abelian setting.
- The paper studies the isomonodromy foliation on moduli of flat rank-\(r\) bundles over \(X/S\).
- It proves that if the p-curvature vanishes mod p for infinitely many primes, then the action of \(\pi1(S,s)\) on rank-\(r\) integral characters of \(\pi1(Xs)\) factors through a finite group.
- The authors say this yields many new cases of the Bost/Ekedahl–Shepherd-Barron–Taylor conjecture.
- The proof uses non-abelian versions of Katz’s formula and the Hodge index theorem.
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