Bernstein-Sato theory for singular rings in positive characteristic

The Bernstein-Sato polynomial is an important invariant of element or ideal in a ring power series characteristic zero, with interesting connections to various algebraic and topological aspects the singularities vanishing locus. Work Mustaţă, later extended by Bitoun third author, provides analogous theory for regular rings positive characteristic. In this paper, we extend singular ambient We establish finiteness rationality results roots large classes rings, relate these other numerical invariants defined via Frobenius map. also obtain number new simplified arguments case.