动机函子锥谱序列;函数域上同调的直和项
Motivically functorial coniveau spectral sequences; direct summands of cohomology of function fields
摘要：
我们构建了一个“三角模拟"coniveau谱序列：主题的各种可数字段是”分解“（在这个意义上的Postnikov塔）到扭曲（共）动机的点，这是广义任意Voevodsky的动机。为此，我们构建了一个'Gersten'的重量结构的一定的三角范畴的'comotives'：后者被定义为包含comotives的所有投射极限的光滑簇的重量结构的定义在前面的文件中介绍。相应的权重谱序列本质上是coniveau 1;它们是$DM^{eff}_{gm}$ -函子（从$E_2$开始），并且可以根据类别$DM^-_{eff}$的同伦$t$ -结构来计算（类似于光滑簇的情况）。这就把Bloch和Ogus开创性的coniveau谱序列计算扩展到动机上。我们还得到了一个光滑的半局部计划的上同调是一个直接和的上同调的一般纤维;上同调的函数域包含扭曲的上同调的剩余域（所有的几何赋值）。我们还进一步发展的一般理论的重量结构的三角范畴（独立于“动机”的一部分文件）。此外，我们还发展了一个关于三角范畴的“好”配对的理论，这似乎是一个新的课题。
英文摘要：
We construct a 'triangulated analogue' of coniveau spectral sequences: the motif of a variety over a countable field is 'decomposed' (in the sense of Postnikov towers) into the twisted (co)motives of its points; this is generalized to arbitrary Voevodsky's motives. To this end we construct a 'Gersten' weight structure for a certain triangulated category of 'comotives': the latter is defined to contain comotives for all projective limits of smooth varieties; the definition of a weight structure was introduced in a preceding paper. The corresponding weight spectral sequences are essentially coniveau one; they are $DM^{eff}_{gm}$-functorial (starting from $E_2$) and can be computed in terms of the homotopy $t$-structure for the category $DM^-_{eff}$ (similarly to the case of smooth varieties). This extends to motives the seminal coniveau spectral sequence computations of Bloch and Ogus. We also obtain that the cohomology of a smooth semi-local scheme is a direct summand of the cohomology of its generic fibre; cohomology of function fields contain twisted cohomology of their residue fields (for all geometric valuations). We also develop further the general theory of weight structures for triangulated categories (independently from the 'motivic' part of the paper). Besides, we develop a certain theory of 'nice' pairings of triangulated categories; this subject seems to be new.
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