TY - JOUR

T1 - Congruence for rational points over finite fields and coniveau over local fields

AU - Esnault, Helene

AU - Xu, Chenyang

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2009/5

Y1 - 2009/5

N2 - 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.

AB - 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.

KW - Congruence

KW - Coniveau

KW - Rational point

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U2 - 10.1090/S0002-9947-08-04629-1

DO - 10.1090/S0002-9947-08-04629-1

M3 - Article

AN - SCOPUS:77950569837

VL - 361

SP - 2679

EP - 2688

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -