2026/06/16 by Manuel Blickle, Daniel Fink
Mathematics · Computer Science · #Rings, Modules, and Algebras #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms
paper · doi:10.1016/j.aim.2026.111105
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 \citepGab04, which states that any Noetherian F-finite ring is a quotient of a regular Noetherian F-finite ring.