Bernstein-Sato theory for arbitrary ideals in positive characteristic

Bernstein–sato Roots for Monomial Ideals in Positive Characteristic

“…We begin by reviewing the notion of Bernstein-Sato root from [QG19], to which we refer the reader for details. Let k be a perfect field of characteristic p > 0 and R be a regular k-algebra that is essentially of finite-type.…”

“…In [QG19] the approaches of Mustat ¸ȃ and Bitoun were expanded to arbitrary ideals a ⊆ R and, in particular, a notion of Bernstein-Sato root of a is defined by generalizing a previous definition of Bitoun. These Bernstein-Sato roots are characteristic-p analogues of the roots of the Bernstein-Sato polynomial (it is a question in [QG19] whether one can find an analogue for the multiplicity of a root).…”

“…The Bernstein-Sato roots of a are negative, lie in Z (p) and encode some information about the F -jumping numbers of a [QG19]. They are also somewhat compatible with reduction from characteristic zero [QG].…”

“…Our proof relies heavily on results from [BMS06b]. In Section 2 we review the notion of Bernstein-Sato root as defined in [QG19] as well as the needed theorems from [BMS06b]. We then prove our result in Section 3.…”