Work

L-smooth factorization for Noetherian F-finite rings

Year: 2026

Type: article

Abstract: We show that any homomorphism between Noetherian $F$-finite rings can be factored into a regular morphism between Noetherian $F$-finite rings followed by a surjection. This result establishes an analog of the 'smooth-by-surjective' factorization for finite type maps. As part of our analysis, we observe that for maps of Noetherian $F$-finite rings, regularity and formal smoothness are both equivalent to $L$-smoothness, meaning that the cotangent complex, as in the smooth case, is a locally free module of finite rank concentrated in degree zero. Our findings may also be viewed as a relative version of Gabber's final remark in \citep{Gab04}, which states that any Noetherian $F$-finite ring is a quotient of a regular Noetherian $F$-finite ring.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2026.111105

Authors: Manuel Blickle, Daniel Fink

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funder: Deutsche Forschungsgemeinschaft

Award: TRR 326: Geometrie und Arithmetik uniformisierter Strukturen (GAUS)