标题： 强A^1不变层（继F. Morel之后） 显示英文标题

标题： Strongly A^1-invariant sheaves (after F. Morel)

摘要： 强（分别地严格）A1-不变的层是域上动机同伦理论的基础。它们是光滑代数簇在域k上的Nisnevich拓扑上的（阿贝尔）群层，具有这样的性质：当用X上的仿射直线替换一个代数簇X时，它们的零阶和一阶Nisnevich上同调集（分别地所有Nisnevich上同调群）保持不变。Fabien Morel的一个著名定理指出，如果基域k是完美域，那么任何强A1-不变的阿贝尔群层自动是严格A1-不变的。这些讲义的目标有两个：（1）提供这个结果的完整证明，（2）概述一些其应用。 显示英文摘要

摘要： Strongly (respectively strictly) A1-invariant sheaves are foundational for motivic homotopy theory over fields. They are sheaves of (abelian) groups on the Nisnevich site of smooth varieties over a field k, with the property that their zeroth and first Nisnevich cohomology sets (respectively all Nisnevich cohomology groups) are invariant under replacing a variety X by the affine line over X. A celebrated theorem of Fabien Morel states that if the base field k is perfect, then any strongly A1-invariant sheaf of abelian groups is automatically strictly A1-invariant. The aim of these lecture notes is twofold: (1) provide a complete proof if this result, and (2) outline some of its applications.