Congruence for rational points over finite fields and coniveau over local fields
Hélène Esnault, Chenyang Xu
Number | 9 |
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Author | Hélène Esnault |
Year | 2007 |
If the ell-adic cohomology of a projective smooth variety, defined over a local field K with finite residue field k, is supported in codimension ≥ 1 then every model over the ring of integers of K has a k-rational point. For K a p-adic field, this is [8, Theorem 1.1]. If the model X is regular, one has a congruence |X (k)| ≡ 1 modulo |k| for the number of k-rational points ([7, Theorem 1.1]). The congruence is violated if one drops the regularity assumption.