Abstract
For a Jacobian elliptic surface over a finite field and a prime different from the characteristic of , the points of period on the smooth fibers of yield, for each , a smooth projective curve over by taking Zariski closure in and normalization. We consider the restriction map in -adic étale cohomology . By using an earlier result of ours we prove that, except for at most a finite number of such primes , this map is faithful on the submodule of those classes vanishing on the geometric fibers and on the zero section of , and that it gives an isomorphism between this submodule and the subgroup of of primitive elements in the sense of Serre.
Citation
Gerald E. Welters. "On the -adic cohomology of Jacobian elliptic surfaces over finite fields." Kyoto J. Math. 56 (4) 745 - 783, December 2016. https://doi.org/10.1215/21562261-3664905
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