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

  title={Kontsevich's conjecture on an algebraic formula for vanishing cycles of local systems},
  author={Claude Sabbah and Morihiko Saito},
  journal={arXiv: Algebraic Geometry},
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… Expand
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