摘要翻译：
本文致力于赋权结构的三角范畴（一个新的概念，D.Pauksztello已经独立地将它们作为共T结构引入）。这公理了$k(B)$中复形愚蠢截断的性质。我们还为Voevodsky的动机类别和各种光谱类别构造了权重结构。重量结构$W$定义对象的Postnikov塔；这些塔是标准的和泛函的“直到上同调上为零的态射”。由于$Hw$是$W$（在$DM_{gm}$中我们有$Hw=Chow$)的中心，我们定义了一个规范保守的弱精确函子$T$从我们的$C$到某个弱复形的范畴$K_W(Hw)$。对于任意(co)同调函子$H:C\to a$对于阿贝尔函数$a$我们构造了一个权谱序列$T:H(X^i[j])\蕴涵H(X[i+j])$,其中$(X^i)=T(X)$；它是从$E_2$开始的规范的和功能的。这种谱序列专门用于动机的经典实现的“通常”(Deligne's）加权谱序列和光谱的Atiyah-Hirzebruch谱序列。在一定的限制条件下，我们证明了$K_0(C)\cong K_0(Hw)$和$K_0(End C)\cong K_0(End Hw)$。权重结构的定义与T型结构的定义几乎是双重的；但有几个属性不同。人们通常可以构造一个与$W$“相邻”的$T$-结构，反之亦然。对于Voevodsky的$dm^{eff}-$（我们得到了某些新的Chow权重和T-结构；后者的核心是对偶的，$Chow{eff}$)和稳定同伦范畴都是如此。Chow T结构与未分支上同调密切相关。
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英文标题：
《Weight structures vs. $t$-structures; weight filtrations, spectral
  sequences, and complexes (for motives and in general)》
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作者：
M.V. Bondarko
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最新提交年份：
2016
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分类信息：

一级分类：Mathematics        数学
二级分类：K-Theory and Homology        K-理论与同调
分类描述：Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
代数和拓扑K-理论，与拓扑的关系，交换代数和算子代数
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Algebraic Topology        代数拓扑
分类描述：Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论，同调代数，流形的代数处理
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英文摘要：
  This paper is dedicated to triangulated categories endowed with weight structures (a new notion; D. Pauksztello has independently introduced them as co-t-structures). This axiomatizes the properties of stupid truncations of complexes in $K(B)$. We also construct weight structures for Voevodsky's categories of motives and for various categories of spectra. A weight structure $w$ defines Postnikov towers of objects; these towers are canonical and functorial 'up to morphisms that are zero on cohomology'. For $Hw$ being the heart of $w$ (in $DM_{gm}$ we have $Hw=Chow$) we define a canonical conservative 'weakly exact' functor $t$ from our $C$ to a certain weak category of complexes $K_w(Hw)$. For any (co)homological functor $H:C\to A$ for an abelian $A$ we construct a weight spectral sequence $T:H(X^i[j])\implies H(X[i+j])$ where $(X^i)=t(X)$; it is canonical and functorial starting from $E_2$. This spectral sequences specializes to the 'usual' (Deligne's) weight spectral sequences for 'classical' realizations of motives and to Atiyah-Hirzebruch spectral sequences for spectra. Under certain restrictions, we prove that $K_0(C)\cong K_0(Hw)$ and $K_0(End C)\cong K_0(End Hw)$.   The definition of a weight structure is almost dual to those of a t-structure; yet several properties differ. One can often construct a certain $t$-structure which is 'adjacent' to $w$ and vice versa. This is the case for the Voevodsky's $DM^{eff}_-$ (one obtains certain new Chow weight and t-structures for it; the heart of the latter is 'dual' to $Chow^{eff}$) and for the stable homotopy category. The Chow t-structure is closely related to unramified cohomology.
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PDF链接：
https://arxiv.org/pdf/0704.4003