New Results on Weight-Two Motivic Cohomology
New Results on Weight-Two Motivic Cohomology
复制标题
权重二动机上同调的新结果
DOI：
10.1007/978-0-8176-4576-2_2
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发表时间：
1990
影响因子：
1.8
通讯作者：
S. Lichtenbaum
中科院分区：
文献类型：
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作者：
S. Lichtenbaum
在Grothendieck对代数几何的众多贡献中，他强调寻找代数簇的泛上同调理论，并根据动机对其进行猜想描述[Ma]。最近，许多作者开始描述并猜想地定义了代数簇的上同调理论，Beilinson，MacPherson和Scheck htman([BMS]，[BE]，[Bl]，[T]，[L1]，[L2])将其命名为“Motivic上同调”。人们希望，当这一理论得到充分发展时，它将在某种意义上具有普遍性，从而至少部分地回答了格罗森迪克的问题。
Among Grothendieck’s manifold contributions to algebraic geometry is his emphasis on the search for a universal cohomology theory for algebraic varieties and a conjectured description of it in terms of motives [Ma]. Various authors have recently set out to describe the properties of and conjecturally define a cohomology theory for algebraic varieties, which has been baptized “motivic cohomology” by Beilinson, MacPherson, and Schechtman ([BMS],[Be],[Bl],[T],[L1],[L2]). It is hoped that this theory, when and if it is fully developed, will in some sense be universal and thus provide at least a partial response to Grothendieck’s question.