2024/03/19 by Jack Jeffries, Jeffries, Jack, David I. Lieberman +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #Commutative Algebra (math.AC) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2403.13146
openalex publication_date 2024/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bernstein's inequality is a central result in the theory of D-modules on smooth varieties. While Bernstein's inequality fails for rings of differential operators on general singularities, recent work of Àlvarez Montaner, Hernández, Jeffries, Núñez-Betancourt, Teixeira, and Witt establishes Bernstein's inequality for invariants of finite groups in characteristic zero and certain other mild singularities in positive characteristic. Motivated by extending this result to new classes of singular rings, we introduce a ``two-sided'' analogue of the Bernstein-Sato polynomial which we call the sandwich Bernstein-Sato polynomial. We apply this notion to give an effective criterion to verify Bernstein's inequality, and apply this to show that Bernstein's inequality holds for the coordinate ring of ℙa × ℙb via the Segre embedding. We also establish a number of examples and basic results on sandwich Bernstein-Sato polynomials.