Personal tools
You are here: Home Publications Congruence for rational points over finite fields and coniveau over local fields

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

Hélène Esnault, Chenyang Xu

Number 9
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.

More information about this publication…

Document Actions