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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]

References

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  1. ^ Fu, Lei (30 December 2013). "A Thom-Sebastiani Theorem in Characteristic p". arXiv:1105.5210. {{cite journal}}: Cite journal requires |journal= (help)
  2. ^ a b Illusie 2016, § 0.
  3. ^ Sebastiani, M.; Thom, R. (1971). "Un résultat sur la monodromie". Inventiones Mathematicae. 13 (1–2): 90–96. Bibcode:1971InMat..13...90S. doi:10.1007/BF01390095. S2CID 121578342.