Coniveau over $p$-adic fields and points over finite fields

Details Coniveau over $p$-adic fields and points over finite fields Coniveau over $p$-adic fields and points over finite fields

2007-04-10

arxiv.org/abs/0704.1273v1

Mathematics

Number Theory

5 pages

Scientific paper

If the $\ell$-adic cohomology of a projective smooth variety, defined over a $\frak{p}$-adic field $K$ with finite residue field $k$, is supported in codimension $\ge 1$, then any model over the ring of integers of $K$ has a $k$-rational point. This slightly improves our earlier result math/0405318: we needed there the model to be regular (but then our result was more general: we obtained a congruence for the number of points, and $K$ could be local of characteristic $p>0$).

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