Weight structures and 'weights' on the hearts of $t$-structures
Weight structures and 'weights' on the hearts of $t$-structures
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权重结构和 $t$ 结构的核心“权重”
DOI：
10.4310/hha.2012.v14.n1.a12
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
M. Bondarko
中科院分区：
文献类型：
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作者：
M. Bondarko
我们定义和研究横向重量和t-结构（三角范畴）;如果重量结构是横向的t-one，那么它定义了一定的“重量”的心脏。我们的结果公理化并详细描述了Voevodsky动机的Chow权重结构wChow（在前面的论文中介绍）、（推测的）动机t结构以及它们的推测权重过滤之间的关系。这幅图变得非结构性时，限制到衍生类别的德利涅的1-动机（在一个光滑的基础）和阿廷泰特动机的号码字段。特别是，我们证明了Voevodsky的动机（这是由wChow）的“权重”是兼容的1-动机（这是“经典”定义使用一个相当不同的方法），这一结果是新的。对于Beilinson的D H H H P（分次可极化混合Hodge复形的衍生范畴）和（Saito的）混合Hodge模的衍生范畴，也存在横切于规范t-结构的权结构。我们还研究了t的心的权过滤和权谱序列的退化。t和w之间的对应关系严格弱于横截性;然而它更容易检查，并且我们仍然得到严格受态射尊重的t的心（的对象）的某种过滤。在随后的论文中，我们应用所获得的结果，以减少存在的Beilinson的混合motivic层（在一个基本计划S）和'重量'，他们（某些）标准motivic aestructions在一个通用的域K。
We define and study transversal weight and t-structures (for triangulated categories); if a weight structure is transversal to a t-one, then it defines certain ‘weights’ for its heart. Our results axiomatize and describe in detail the relations between the Chow weight structure wChow for Voevodsky’s motives (introduced in a preceding paper), the (conjectural) motivic t-structure, and the conjectural weight filtration for them. This picture becomes non-conjectural when restricted to the derived categories of Deligne’s 1-motives (over a smooth base) and of Artin-Tate motives over number fields. In particular, we prove that the ‘weights’ for Voevodsky’s motives (that are given by wChow) are compatible with those for 1-motives (that were ‘classically’ defined using a quite distinct method); this result is new. Weight structures transversal to the canonical t-structures also exist for the Beilinson’s D H̃p (the derived category of graded polarizable mixed Hodge complexes) and for the derived category of (Saito’s) mixed Hodge modules. We also study weight filtrations for the heart of t and (the degeneration of) weight spectral sequences. The corresponding relation between t and w is strictly weaker than transversality; yet it is easier to check, and we still obtain a certain filtration for (objects of) the heart of t that is strictly respected by morphisms. In a succeeding paper we apply the results obtained in order to reduce the existence of Beilinson’s mixed motivic sheaves (over a base scheme S) and ‘weights’ for them to (certain) standard motivic conjectures over a universal domain K.