POLES OF ZETA FUNCTIONS OF COMPLETE INTERSECTIONS |
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Authors: | WAN Daqing |
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Affiliation: | Department of Mathematics, University of California, Irvine, CA 92697-3875, USA |
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Abstract: | A vanishing theorem is proved for e-adic cohomology with compact support on an affine (singular) complete intersection. As an application, it is shown that for an affine complete intersection defined over a finite field 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-divisibiliy of the poles or equivalently an improvement of the polar part of the AxKatz theorem for an affine complete intersection. Similar results hold for a projective complete intersection. |
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Keywords: | Pole Zeta function Complete intersection |
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