论文标题
在第二个L-Adic Bloch图的图像上
On the image of the second l-adic Bloch map
论文作者
论文摘要
对于在完美领域上定义的平滑射击几何未释放的三倍，我们表明，在该领域中存在一个规范的Abelian品种，即第二个代数代表，其理性泰特泰特（Tate）模型在规范上是所有Prime l for All Prime l的第三个L-ADIC COLOMOGY群体。另外，存在诱导这些标识的合理对应关系。在几何理性链相关的种类的情况下，一个人在第二代数代表的积分模块与该品种的第三个L-ADIC共同体学组之间获得了规范的识别，如果该品种是一个稳定的稳定的三倍，则这些识别是由集成对应的诱导的。我们的整体策略在于研究 - 对于任意的平滑投射品种，第二个Ell-Adic Bloch地图的图像限于“信函（CO）Niveau Feltration”。这补充了由于SUWA引起的合理系数。在附录中，我们回顾了Bloch地图及其基本属性的构建。
For a smooth projective geometrically uniruled threefold defined over a perfect field we show that there exists a canonical abelian variety over the field, namely the second algebraic representative, whose rational Tate modules model canonically the third l-adic cohomology groups of the variety for all primes l. In addition, there exists a rational correspondence inducing these identifications. In the case of a geometrically rationally chain connected variety, one obtains canonical identifications between the integral Tate modules of the second algebraic representative and the third l-adic cohomology groups of the variety, and if the variety is a geometrically stably rational threefold, these identifications are induced by an integral correspondence. Our overall strategy consists in studying -- for arbitrary smooth projective varieties -- the image of the second ell-adic Bloch map restricted to the Tate module of algebraically trivial cycle classes in terms of the "correspondence (co)niveau filtration". This complements results with rational coefficients due to Suwa. In the appendix, we review the construction of the Bloch map and its basic properties.
