Poles of Zeta Functions of Complete Intersections
نویسنده
چکیده
A vanishing theorem is proved for`-adic cohomology with compact support on a singular aane complete intersection. As an application, it is shown that for an aane complete intersection deened over a nite eld of q elements, the reciprocal \poles" of the zeta function are always divisible by q as algebraic integers. A p-adic proof is also given, which leads to further q-divisibility of the poles or equivalently an improvement of the polar part of the Ax-Katz theorem for an aane complete intersection. Similar results hold for a projective complete intersection.
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