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 language | English (US) |
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Pages (from-to) | 2679-2688 |
Number of pages | 10 |
Journal | Transactions of the American Mathematical Society |
Volume | 361 |
Issue number | 5 |
DOIs | |
State | Published - May 2009 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
Keywords
- Congruence
- Coniveau
- Rational point