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

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 نشر من قبل H\\'el\\`ene Esnault
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English
 تأليف Hel`ene Esnault




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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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