On pristine morphisms

2025/12/05 by Carvajal-Rojas, Javier, Stäbler, Axel
Mathematics · #13A35 #14B25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.06063

openalex publication_date 2025/12/05 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28

Abstract

We investigate flat morphisms of schemes of positive characteristic whose relative Frobenius is an isomorphism, which we call pristine. We show that these give rise to a natural Grothendieck topology that is fine tuned for the localization of Cartier modules.

Citations

• Relative Inverse Limit Perfection of Derived Commutative Rings
• Formally regular rings and descent of regularity
• Functorial Test Modules
• V-filtrations in positive characteristic and test modules
• The pro-étale topology for schemes
• F-finiteness of homomorphisms and its descent

Related

• Local structure theorems for smooth maps of formal schemes
• Infinitesimal local study of formal schemes
• Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes
• Smooth Formal Embeddings and the Residue Complex
• Arithmetic D-modules on locally noetherian formal schemes