Thom–Sebastiani Theorem
In complex analysis, a branch of mathematics, the Thom–Sebastiani Theorem states: given the germ  defined as  where  are germs of holomorphic functions with isolated singularities, the vanishing cycle complex of  is isomorphic to the tensor product of those of . Moreover, the isomorphism respects the  monodromy operators in the sense: . The theorem was introduced by Thom and Sebastiani in 1971. Observing that the analog fails in positive characteristic, Deligne suggested that, in positive characteristic, a tensor product should be replaced by a (certain) local convolution product. References 

Theorems in complex analysis