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This partly expository paper investigates versions of the Tate conjecture onthe cycle map for varieties defined over finite fields with values in 'etalecohomology with Z_\ell-coefficients. The bulk of the paper is an exposition ofa 1998 result of C. Schoen which shows that an integral version of theconjecture holds for 1-cycles provided the usual conjecture is true fordivisors on surfaces. In a last section we then derive from Schoen's theoremnew results on the existence of degree one zero-cycles on varieties definedover the function field of a smooth proper curve C over the algebraic closureof a finite field. In particular, we show that if the variety in question is asmooth projective complete intersection of dimension at least 3 and of degreeprime to the characteristic, then a zero-cycle of degree one exists if the Tateconjecture is true for divisors on surfaces and the variety extends to a properfibration over C all of whose fibres possess a component of multiplicity one.

Autour de la conjecture de Tate `a coefficients Z_l pour les vari'et'es sur les corps finis