论文标题
塔纳基人的动机类别
Graded-Tannakian categories of motives
论文作者
论文摘要
鉴于刚性张量的三角形类别和矢量空间值的同源函数，昆纳斯同构构成，我们构建了一个普遍的渐变塔纳基人类别，通过该类别，给定的同源函数因素。我们将其用于（无条件地）构建与固定的Weil共同体学理论相关的纯粹动机等级的Tarnakian类别，并且具有纤维函子，实现了给定的共同体学理论。对于$ \ ell $ -ADIC的共同体学和在有限领域代数的地面场，此类别是Tannakian。在这种情况下，我们特别获得动机galois群体，它们自然地在$ \ ell $ - adic的共同体上行动，而无需假设任何标准猜想。我们表明，如果标准猜想d成立，这些分级的Tannakian类别等于Grothendieck的纯粹动机类别。
Given a rigid tensor-triangulated category and a vector space valued homological functor for which the Künneth isomorphism holds, we construct a universal graded-Tannakian category through which the given homological functor factors. We use this to (unconditionally) construct graded-Tannakian categories of pure motives associated to a fixed Weil cohomology theory, with a fiber functor realizing the given cohomology theory. For $\ell$-adic cohomology and a ground field which is algebraic over a finite field, this category is Tannakian. In this case, we obtain in particular motivic Galois groups which act naturally on $\ell$-adic cohomology without assuming any of the standard conjectures. We show that these graded-Tannakian categories are equivalent to Grothendieck's category of pure motives if the standard conjecture D holds.
