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 .{{cite journal |last1=Fu |first1=Lei |title=A Thom-Sebastiani Theorem in Characteristic p |date=30 December 2013 |arxiv=1105.5210 }} Moreover, the isomorphism respects the monodromy operators in the sense: .{{harvnb|Illusie|2016|loc=§ 0.}}
The theorem was introduced by Thom and Sebastiani in 1971.{{cite journal |last1=Sebastiani |first1=M. |last2=Thom |first2=R. |title=Un résultat sur la monodromie |journal=Inventiones Mathematicae |date=1971 |volume=13 |issue=1–2 |pages=90–96 |doi=10.1007/BF01390095 |bibcode=1971InMat..13...90S |s2cid=121578342 }}
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
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- {{cite journal |last1=Illusie |first1=Luc |title=Around the Thom-Sebastiani theorem |date=24 April 2016 |arxiv=1604.07004 }}
Category:Theorems in complex analysis
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