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 local convolution product.