2018/11/27 by Alessandro De Stefani, De Stefani, Alessandro, Thomas Polstra +3
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.1811.11022
31 pages
arxiv created 2018/11/27 · openalex publication_date 2018/11/27 · arxiv updated 2018/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the notion of Frobenius Betti numbers and F-splitting ratio to large classes of finitely generated modules over rings of prime characteristic, which are not assumed to be local. We also prove that the strong F-regularity of a pair (R,\mathscrD), where \mathscrD is a Cartier algebra, is equivalent to the positivity of the global F-signature \rm s(R,\mathscrD) of the pair. This extends a result previously proved by these authors, by removing an extra assumption on the Cartier algebra.