A cohomological characterization of Alexander schemes
A cohomological characterization of Alexander schemes
复制标题
亚历山大方案的上同调表征
DOI：
10.1007/s002220050336
复制
发表时间：
1999
影响因子：
3.1
通讯作者：
Shungen Kimura
中科院分区：
文献类型：
--
作者：
Shungen Kimura
Vistoli从具有q -系数的交理论的观点出发，在[19]中定义了表现为光滑变型的Alexander格式。本文将肯定地回答Vistoli关于Alexander性质是Zariski局部的猜想。主要的工具是双变捆的阿贝尔范畴，我们将花大部分时间来证明这个范畴的基本性质。我们证明了一个方案是Alexander当且仅当双变轴的所有第一上同群消失，这是Serre定理的一个类比，Serre定理说一个方案是仿射当且仅当拟相干轴的所有第一上同群消失。Serre定理表明仿射闭子方案的并集也是仿射的。我们将逐行模拟证明，证明Alexander开子方案的并集也是Alexander。
Vistoli defined Alexander schemes in [19], which behave like smooth varieties from the viewpoint of intersection theory with Q-coefficients. In this paper, we will affirmatively answer Vistoli’s conjecture that Alexander property is Zariski local. The main tool is the abelian category of bivariant sheaves, and we will spend most of our time for proving basic properties of this category. We show that a scheme is Alexander if and only if all the first cohomology groups of bivariant sheaves vanish, which is an analogy of Serre’s theorem, which says that a scheme is affine if and only if all the first cohomology groups of quasi-coherent sheaves vanish. Serre’s theorem implies that the union of affine closed subschemes is again affine. Mimicking the proof line by line, we will prove that the union of Alexander open subschemes is again Alexander.
与阿贝尔变种的对应关系
DOI：
--
发表时间：
2006
期刊：
II, Hiroshima Math.J. 35
影响因子：
--
作者：
Masayuki Hirokado;Hiroyuki Ito,Natsuo Saito;Masayuki Hirokado;Atsushi Shiho;Kazuhiro Fujiwara;Fumiharu Kato;中島 幸喜;Shun-ichi Kimura;Yukiyoshi Nakajima;Shunichi Kimura
通讯作者：
Shunichi Kimura