On the tensor property of Bernstein-Sato polynomials

We prove the multiplicative Thom–Sebastiani rule for Bernstein–Sato polynomials, thereby answering a long-standing question of Budur and Popa. This result is extended to the tensor product of two effective divisors on the product of two arbitrary nonsingular complex varieties. As a consequence, we also derive a multiplicative Thom-Sebastiani type result for the strong monodromy conjecture. Furthermore, we propose analogous conjectures for Bernstein–Sato polynomials for ideals and verify them in the case of monomial ideals.