Thom–Sebastiani Theorem
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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 .[1] Moreover, the isomorphism respects the monodromy operators in the sense: .[2]
The theorem was introduced by Thom and Sebastiani in 1971.[3]
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.[2]