Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Monday, 24 September 2007, 16:00-17:00, room 401.

Professor Shun-ichi Kimura (Hiroshima University): Rationality of the motivic zeta and the Nilpotency theorem

Abstract:

In my talk in June 20th, we discussed the notion of the finite dimensionality of motives and its consequences. In this talk, we approach the same phenomenon from a different view point, namely the rationality of the Motivic zeta. An important ingredient of Weil conjecture is the rationality of the Weil zeta function, which was generalized to the rationality of the Motivic zeta for the case of curves by Kapranov. We prove that the finite dimensionality of the motive implies the rationality of the Motivic zeta in general. We also give some details of a proof of nilpotency theorem.