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中科院数学与系统科学研究院

数学研究所

中科院晨兴数学中心

 

学术报告会

 

Speaker  Luc Illusie(Université Paris-Sud)

TitleNearby cycles over general bases and Thom-Sebastiani theorems

Time2016.1.8 14:00-16:00

2016.1.12 14:00-16:00

2016.1.15 14:00-16:00

2016.1.19 14:00-16:00

VenueN913

Abstract:

   For germs of holomorphic functions f: Cm+1C, g: Cn+1C having an isolated critical point at 0 with value 0, the classical Thom-Sebastiani theorem describes the vanishing cycles group Φm+n+1(fg) (and its monodromy) as a tensor product Φm(f)Φn(g), where (fg)(x,y)=f(x)+g(y), x=(x0,...,xm), y=(y0,...,yn). I will discuss algebraic variants and generalizations of this result over fields of any characteristic, where the tensor product is replaced by a certain local convolution product, as suggested by Deligne. The main theorem is a Künneth formula for RΨ in the framework of Deligne's theory of nearby cycles over general bases.

 

Plan:

1. Review of classical nearby and vanishing cycles

2. Deligne's oriented products and nearby cycles over general bases

3. Ψ-goodness and Künneth theorems

4. Review of global and local additive convolution

5. Thom-Sebastiani type theorems

6. The tame case: monodromy and variation

7. Open questions

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