关于不同类型的物体的Tate `a系数Z_1的猜想
Autour de la conjecture de Tate `a coefficients Z_l pour les vari'et'es sur les corps finis
摘要：
本文研究了关于定义在有限域上的簇的圈映射的Tate猜想，其值与Z_ \ell -系数不成余上同调.本文的大部分内容是对C. Schoen这表明，一个完整的版本的猜想持有1-周期提供了通常的猜想是真实的除数的表面。在最后一节中，我们然后从Schoen定理的新结果的存在度一个零圈的品种定义在函数域的光滑的正常曲线C的代数闭包的有限域。特别是，我们表明，如果各种问题是一个光滑的射影完全相交的尺寸至少为3和度素的特点，那么零循环度1存在，如果泰特猜想是真的表面上的因子和各种延伸到一个适当的纤维化C所有的纤维具有一个组件的多重性。
英文摘要：
This partly expository paper investigates versions of the Tate conjecture on the cycle map for varieties defined over finite fields with values in 'etale cohomology with Z_\ell-coefficients. The bulk of the paper is an exposition of a 1998 result of C. Schoen which shows that an integral version of the conjecture holds for 1-cycles provided the usual conjecture is true for divisors on surfaces. In a last section we then derive from Schoen's theorem new results on the existence of degree one zero-cycles on varieties defined over the function field of a smooth proper curve C over the algebraic closure of a finite field. In particular, we show that if the variety in question is a smooth projective complete intersection of dimension at least 3 and of degree prime to the characteristic, then a zero-cycle of degree one exists if the Tate conjecture is true for divisors on surfaces and the variety extends to a proper fibration over C all of whose fibres possess a component of multiplicity one.
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