We survey classical and recent results on symbolic powers of ideals. We focus on properties
and problems of symbolic powers over regular rings, on the comparison of symbolic and …

The F-signature of a local ring of prime characteristic is a numerical invariant that detects
many interesting properties. For example, this invariant detects (non) singularity and strong …

This paper investigates the existence and properties of a Bernstein–Sato functional equation
in nonregular settings. In particular, we construct D-modules in which such formal equations …

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The first author had shown earlier that for a standard graded ring R and a graded ideal I in
characteristic p> 0, with ℓ (R/I)<∞, there exists a compactly supported continuous function f …

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Mustaţă defined Bernstein-Sato polynomials in prime characteristic for principal ideals and
proved that the roots of these polynomials are related to the $ F $-jumping numbers of the …

The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a
polynomial ring or power series ring of characteristic zero, with interesting connections to …

In their work on differential operators in positive characteristic, Smith and Van den Bergh
define and study the derived functors of differential operators; these arise naturally as …

In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-
modules for rings of invariants of finite groups in characteristic zero, and for strongly F …