摘要翻译：
我们把（同调的）动机的权重复合物，从而把Grothendieck动机群中的欧拉特征，与算术变体和Deligne-Mumford栈联系起来；这扩展了Crelle第478卷“下降、动机和K-理论”一文中的结果，其中类似的结果被证明在特征为零的域上的变种。我们使用具有有理系数的K_0动机，而不是Chow动机，因为我们不能诉诸于奇点的解析，而是必须使用de Jong的结果。另外，对于域上的变体，我们证明了权复的逆变性的一个一般结果，特别证明了变体间任何有限维数的态射都会诱导出权复的态射。
---
英文标题：
《Motivic Weight Complexes for Arithmetic Varieties》
---
作者：
Henri Gillet and Christophe Soul\'e
---
最新提交年份：
2009
---
分类信息：

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
--

---
英文摘要：
  We associate weight complexes of (homological) motives, and hence Euler characteristics in the Grothendieck group of motives, to arithmetic varieties and Deligne-Mumford stacks; this extends the results in the paper "Descent, Motives and K-theory" in volume 478 of Crelle, where a similar result was proved for varieties over a field of characteristic zero. We use K_0-motives with rational coefficients, rather than Chow motives, because we cannot appeal to resolution of singularities, but rather must use de Jong's results. In addition, for varieties over a field we prove a general result on contravariance of weight complexes, in particular showing that any morphism of finite tor-dimension between varieties induces a morphism of weight complexes.
---
PDF链接：
https://arxiv.org/pdf/0804.4853