|
|
| |
| POLES OF ZETA FUNCTIONS OF COMPLETE INTERSECTIONS |
| |
Citation： |
WAN Daqing.POLES OF ZETA FUNCTIONS OF COMPLETE INTERSECTIONS[J].Chinese Annals of Mathematics B,2000,21(2):187~200 |
| Page view： 1304
Net amount： 917 |
Authors： |
WAN Daqing; |
|
|
| Abstract： |
A vanishing theorem is proved for $\ell$-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 $q$-divisibility of the poles or equivalently an improvement of the polar part of the Ax-
Katz theorem for an affine complete intersection. Similar results hold for a projective complete
intersection. |
Keywords： |
Pole, Zeta function, Complete intersection |
Classification： |
14G10 |
|
|
Download PDF Full-Text
|
|
|
|
