2017/03/21 by Stäbler, Axel
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1703.07391
We show that each direct summand of the associated graded module of the test module filtration τ(M, fλ)λ≥ 0 admits a natural Cartier structure. If λ is an F-jumping number, then this Cartier structure is nilpotent on τ(M, fλ-ε)/τ(M, fλ) if and only if the denominator of λ is divisible by p. We also show that these Cartier structures coincide with certain Cartier structures that are obtained by considering certain D-modules associated to M that were used to construct Bernstein-Sato polynomials. Moreover, we point out that the zeros of the Bernstein-Sato polynomial bM,f attached to an F-regular Cartier module correspond to its F-jumping numbers. This generalizes Theorem 5.4 of arXiv:1402.1333 where a stronger version of F-regularity was used. Finally, we develop a basic theory of non-F-pure modules and prove a weaker connection between Bernstein-Sato polynomials bM,f and Cartier modules (M, κ) for which Mf is F-regular and certain jumping numbers attached to M.