Srinivas–Takagi Hodge-filtration conjecture for reductions to F-nilpotent singularities

Establish the conjectured Hodge-filtration vanishing for complex singularities that reduce to F-nilpotent singularities for all but finitely many prime characteristics.

Background

The paper places F-nilpotent singularities within the broader study of singularities defined by Frobenius actions on local cohomology. It explains that Srinivas and Takagi proposed a conjectural relationship between reduction modulo primes and vanishing properties in the Hodge filtration of complex singularities.

The conjecture is identified as Conjecture H_n of Srinivas–Takagi. The paper further notes that this conjecture is related to an arithmetic variant, Conjecture N_n, and to the Weak-Ordinarity conjecture, linking the problem to the relationship between F-injective and Du Bois singularities. This is an explicitly stated conjectural problem rather than a result proved in the survey.

References

Specifically, they conjecture that complex singularities which reduce to $F$-nilpotent singularities for all but finitely many $p$ satisfies certain vanishing in the Hodge filtration Conj. $H_n$.

— $F$-depth and $F$-nilpotent rings: generalizations and applications  (2609.09558 - Maddox et al., 9 Sep 2026) in Section 1, subsection “F-nilpotent singularities”