Finiteness of leaps of modules of integrable derivations of algebras of finite type

2025/11/30 by Miyamoto, Takuya
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.00690

Abstract

We prove the finiteness of leaps of modules of m-integrable derivations for algebras essentially of finite type and, more generally, for schemes essentially of finite type over an algebraically closed field of positive characteristic. This provides an affirmative answer to a question posed by L. N. Macarro. As an application, we establish the coherence of the module of ∞-integrable derivations.

Citations

• Hasse-Schmidt derivations and locally trivial deformations in positive characteristic
• Finiteness of Leaps in the sense of Hasse-Schmidt of reduced rings
• On the behavior of modules of m-integrable derivations in the sense of Hasse-Schmidt under base change
• Leaps of modules of integrable derivations in the sense of Hasse-Schmidt

Related

• Finiteness of Leaps in the sense of Hasse-Schmidt of reduced rings
• Leaps of modules of integrable derivations in the sense of Hasse-Schmidt
• On the behavior of modules of m-integrable derivations in the sense of Hasse-Schmidt under base change
• Divisorial algebras and modules on schemes
• Locally nilpotent module derivations and the fourteenth problem of Hilbert