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)
Title:Nearby cycles over general bases and Thom-Sebastiani theorems
Time:2016.1.8, 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
Venue:N913
Abstract:
For germs of holomorphic functions f: Cm+1→C, g: Cn+1→C having an isolated critical point at 0 with value 0, the classical Thom-Sebastiani theorem describes the vanishing cycles group Φm+n+1(f⊕g) (and its monodromy) as a tensor product Φm(f)⊗Φn(g), where (f⊕g)(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