Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex
Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex
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积分 Monsky-Washnitzer 上同调和超收敛的 de Rham-Witt 复形
DOI：
10.4310/mrl.2014.v21.n2.a6
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
David Zureick
中科院分区：
文献类型：
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作者：
Christopher Davis;David Zureick
在引入Monsky-Washnitzer上同调群的论文中，Monsky和Washnitzer描述了该定义适用于给出积分上同调群的条件。专家们似乎都知道，它们的构造总是给出定义良好的整数上同调群，但这一事实似乎也没有明确地写在任何地方。本文证明了积分Monsky-Washnitzer上同调群对特征p的完美域上的任何非奇异仿射簇都是定义良好的，并将这些上同调群与超收敛的De Rham-Witt上同调群进行了比较。前面已经证明，如果仿射簇相对于基场的特征具有较小的维度，则上同调群是同构的。我们将这一结果推广到：对于任何非奇异仿射簇，无论其维数如何，积分Monsky-Washnitzer上同调与超收敛De Rham-Witt上同调之间存在同构，其次数相对于特征标度较小。
In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology groups. It seems to be well-known among experts that their construction always gives well-defined integral cohomology groups, but this fact also does not appear to be explicitly written down anywhere. In this paper, we prove that the integral Monsky-Washnitzer cohomology groups are well-defined, for any nonsingular affine variety over a perfect field of characteristic p. We then compare these cohomology groups with overconvergent de Rham-Witt cohomology. It was shown earlier that if the affine variety has small dimension relative to the characteristic of the ground field, then the cohomology groups are isomorphic. We extend this result to show that for any nonsingular affine variety, regardless of dimension, we have an isomorphism between integral Monsky-Washnitzer cohomology and overconvergent de Rham-Witt cohomology in degrees which are small relative to the characteristic.
拉姆-维特上同调的过收敛
DOI：
--
发表时间：
2010
期刊：
Annales Ecole Normale Superieure (to appear)
影响因子：
--
作者：
C Davis
通讯作者：
C Davis