Congruence for rational points over finite fields and coniveau over local fields

Details Congruence for rational points over finite fields and coniveau over local fields Congruence for rational points over finite fields and coniveau over local fields

2007-06-07

arxiv.org/abs/0706.0972v1

Mathematics

Number Theory

8 pages

Scientific paper

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 $\ge 1$, then every model over the ring of integers of $K$ has a $k$-rational point. For $K$ a $p$-adic field, this is math/0405318, Theorem 1.1. If the model $\sX$ is regular, one has a congruence $|\sX(k)|\equiv 1 $ modulo $|k|$ for the number of $k$-rational points 0704.1273, Theorem 1.1. The congruence is violated if one drops the regularity assumption.

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