EVENT DETAILS AND ABSTRACT

Title: Rationality of Zeta Functions via Cutting and Pasting
Speaker: Michael Larsen
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Abstract:

Dwork's theorem asserts that the zeta function of any variety over the field with q elements can be expressed as a rational function in q^{-s}. In the case of curves, Kapranov observed that this is true in a "motivic" sense, which makes sense and continues to hold even for varieties in characteristic zero. He asked whether this remains true for higher dimensional varieties. Valery Lunts and I proved that in general it does not by constructing two very different obstructions, one from birational geometry, and one from Galois representations. This explains, in some sense, why Dwork's theorem was so much harder to prove in higher dimension than in dimension 1.