Bivariant Theories in Motivic Stable Homotopy
Bivariant Theories in Motivic Stable Homotopy
复制标题
动机稳定同伦中的双变理论
DOI：
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发表时间：
2017
影响因子：
0.9
通讯作者：
Frédéric Déglise
中科院分区：
文献类型：
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作者：
Frédéric Déglise
这项工作的目的是研究的概念，双变理论介绍的富尔顿和麦克弗森的背景下，motivic稳定同伦理论，更普遍的是在更广泛的框架格罗滕迪克六函子形式主义。我们介绍了几种双变理论与一个合适的环谱，我们构建了一个系统的方向（称为基本类）的全球完全相交态射之间的任意计划。这个基本类满足所有预期的性质，从经典的交集理论，并导致Gysin态射，黎曼-罗克公式以及对偶语句，有效的一般计划，包括奇异的，而不需要一个基本字段。
The purpose of this work is to study the notion of bivariant theory introduced by Fulton and MacPherson in the context of motivic stable homotopy theory, and more generally in the broader framework of Grothendieck six functors formalism. We introduce several kinds of bivariant theory associated with a suitable ring spectrum and we construct a system of orientations (called fundamental classes) for global complete intersection morphisms between arbitrary schemes. This fundamental classes satisfies all the expected properties from classical intersection theory and lead to Gysin morphisms, Riemann-Roch formulas as well as duality statements, valid for general schemes, including singular ones and without need of a base field.