标题： 康采维奇关于局部系消失循环的代数公式的猜想 显示英文标题

标题： Kontsevich's conjecture on an algebraic formula for vanishing cycles of local systems

摘要： 对于一个局部系统和一个在光滑复代数簇上的函数，我们给出了M. Kontsevich关于使用对应局部自由层的扭曲de Rham复形的正式微局部化在无穷远处具有正则奇点的可积联络的消逝环的公式的猜想证明。 我们还证明了其局部版本，这可以看作是E. Brieskorn在孤立奇点情况下的结果的自然推广。 然后我们将这些结果推广到正则的holonomic D-模的de Rham复形的情况，在这种情况下，我们必须使用与某种形式的微局部微分算子层的张量积，而不是形式完成。 显示英文摘要

摘要： For a local system and a function on a smooth complex algebraic variety, we give a proof of a conjecture of M. Kontsevich on a formula for the vanishing cycles using the twisted de Rham complex of the formal microlocalization of the corresponding locally free sheaf with integrable connection having regular singularity at infinity. We also prove its local version, which may be viewed as a natural generalization of a result of E. Brieskorn in the isolated singularity case. We then generalize these to the case of the de Rham complexes of regular holonomic D-modules where we have to use the tensor product with a certain sheaf of formal microlocal differential operators instead of the formal completion.