论文标题
关于动机综合体的Chow Weight同源性及其与动机同源性的关系
On Chow-weight homology of motivic complexes and its relation to motivic homology
论文作者
论文摘要
我们详细研究了Voevodsky动机复合物的所谓的Chow权威同源性，并将其与动机同源性联系起来。我们概括了早期的结果，并证明了图案$ m $的高级动机同源性群体消失意味着其Chow-Weight同源性的消失以及其重量复杂$ t（m）$的较高术语的有效性属性以及其同胞的较高deligne重量。将此陈述应用于具有紧凑型支持的动机，我们获得了Chow组消失的相似关系，并以紧凑的品种支持。此外，我们证明，如果几何图案的较高动机同源性群体或普遍域上的多样性是扭转（在某个“范围”中），那么这些群体的指数均匀界定。 为了证明我们的主要结果，我们研究了Voevodsky的动机切片。由于切片函子不尊重动机的紧凑性，因此先前的Chow权威同源论文的结果不足以满足我们的目的。这是我们将它们扩展到（$ w_ {Chow} $ - 在下面有限的）动机复合物的主要原因。
We study in detail the so-called Chow-weight homology of Voevodsky motivic complexes and relate it to motivic homology. We generalize earlier results and prove that the vanishing of higher motivic homology groups of a motif $M$ implies similar vanishing for its Chow-weight homology along with effectivity properties of the higher terms of its weight complex $t(M)$ and of higher Deligne weight quotients of its cohomology. Applying this statement to motives with compact support we obtain a similar relation between the vanishing of Chow groups and the cohomology with compact support of varieties. Moreover, we prove that if higher motivic homology groups of a geometric motif or a variety over a universal domain are torsion (in a certain "range") then the exponents of these groups are uniformly bounded. To prove our main results we study Voevodsky slices of motives. Since the slice functors do not respect the compactness of motives, the results of the previous Chow-weight homology paper are not sufficient for our purposes; this is our main reason to extend them to ($w_{Chow}$-bounded below) motivic complexes.
