In complex analysis, a branch of mathematics, the Thom–Sebastiani Theorem states: given the germ
f : (
n
+
defined as
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.
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