论文标题
精致计划的无关共同体学
Refined unramified cohomology of schemes
论文作者
论文摘要
我们介绍了代数方案的精制未遵循的共同体学的概念，并证明了比较定理，这些定理识别了其中一些具有循环基团的群体。这将恢复平滑的射影品种的低复合循环，以前的Bloch-ogus，colliot-thélène-voisin，Kahn，Voisin和Ma。我们将方法与Voevodsky证明的Bloch-Kato猜想相结合，以表明，在平滑的复杂投影品种中，与琐碎的Abel-Jacobi不变性的任何同源性琐碎的扭转循环具有Coniveau 1。我们进一步表明，同源性繁琐的扭转循环模量代数等效性具有有限的过滤（通过Coniveau），使得分级的商由我们构造的较高的Abel-Jacobi不变性确定。这可以看作是扭转循环模量代数等价的变体。我们还证明了这些结果的$ \ ell $ - adic类似物，其中包含所有$ \ ell $ - $ - power的统一根。
We introduce the notion of refined unramified cohomology of algebraic schemes and prove comparison theorems that identify some of these groups with cycle groups. This recovers for cycles of low codimensions on smooth projective varieties previous results of Bloch--Ogus, Colliot-Thélène--Voisin, Kahn, Voisin, and Ma. We combine our approach with the Bloch--Kato conjecture, proven by Voevodsky, to show that on a smooth complex projective variety, any homologically trivial torsion cycle with trivial Abel--Jacobi invariant has coniveau 1. This establishes a torsion version of a conjecture of Jannsen originally formulated with rational coefficients. We further show that the group of homologically trivial torsion cycles modulo algebraic equivalence has a finite filtration (by coniveau) such that the graded quotients are determined by higher Abel--Jacobi invariants that we construct. This may be seen as a variant for torsion cycles modulo algebraic equivalence of a conjecture of Green. We also prove $\ell$-adic analogues of these results over any field which contains all $\ell$-power roots of unity.
