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

Helene Esnault, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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 ≥ 1, then every model over the ring of integers of K has a k-rational point. For K a p-adic field, this is proved in (Esnault, 2007, Theorem 1.1). If the model χ is regular, one has a congruence |χ(k)| ≡ 1 modulo |k| for the number of k-rational points (Esnault, 2006, Theorem 1.1). The congruence is violated if one drops the regularity assumption.

Original languageEnglish (US)
Pages (from-to)2679-2688
Number of pages10
JournalTransactions of the American Mathematical Society
Volume361
Issue number5
DOIs
StatePublished - May 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Congruence
  • Coniveau
  • Rational point

Fingerprint Dive into the research topics of 'Congruence for rational points over finite fields and coniveau over local fields'. Together they form a unique fingerprint.

Cite this