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La conjecture de Tate entière pour les cubiques de dimension quatre
- Part of
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 2 / February 2015
- Published online by Cambridge University Press:
- 16 October 2014, pp. 253-264
- Print publication:
- February 2015
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- Article
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We prove the integral Tate conjecture for cycles of codimension
$2$ on smooth cubic fourfolds over an algebraic closure of a field finitely generated over its prime subfield and of characteristic different from 
$2$ or 
$3$. The proof relies on the Tate conjecture with rational coefficients, proved in that setting by the first author, and on an argument of Voisin coming from complex geometry.
