If the ℓ-adic cohomology of a projective smooth variety, defined over a p-adic field K with finite residue field k, is supported in codimension ⩾1, then any model over the ring of integers of K has a k-rational point.

Received: 2007-04-26
Accepted: 2007-05-06
Published online: 2007-07-05
DOI: 10.1016/j.crma.2007.05.017

@article{CRMATH_2007__345_2_73_0,
     author = {H\'el\`ene Esnault},
     title = {Coniveau over $ \mathfrak{p}$-adic fields and points over finite fields},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {73--76},
     publisher = {Elsevier},
     volume = {345},
     number = {2},
     year = {2007},
     doi = {10.1016/j.crma.2007.05.017},
     language = {en},
}

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Hélène Esnault. Coniveau over $ \mathfrak{p}$-adic fields and points over finite fields. Comptes Rendus. Mathématique, Volume 345 (2007) no. 2, pp. 73-76. doi : 10.1016/j.crma.2007.05.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.017/