Roots of Bernstein-Sato polynomials for monomial ideals: a positive characteristic approach

We describe the roots of the Bernstein-Sato polynomial of a monomial ideal using reduction mod p and invariants of singularities in positive chracteristic. We give in this setting a positive answer to a problem of Takagi, Watanabe and the second author, concerning the dependence on the characteristic for these invariants of singularities.