Congruence 
for rational points over finite fields and coniveau over
local fields -- Chenyang Xu, February 1, 2008

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If the l-adic cohomology of a projective smooth variety,
defined over a local field K with finite residue field k, is supported
in codimension at least 1, we prove that every model over the ring of integers
of K has a k-rational point. If the model X is regular, one has a
congruence |X(k)| ~ 1  modulo |k| for the number of k-rational
points.  We show by example that the congruence is violated if one drops the
regularity assumption.