论文标题
A^1-euler类：六个函子形式主义，二元性，完整性和完整交集的线性子空间
A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections
论文作者
论文摘要
我们将各种欧拉类别的代数矢量束等等同，包括[BM，KW，DJK]的各个类别，以及M.J. Hopkins，A。Raksit和J.-P。建议的一类。塞雷。我们为这个Euler类建立了整体结果，并在孤立零的局部指数中为局部指数提供了公式，既有6个符合的均匀滑轮的形式主义，又是Scheja和Storch的交换代数的明确配方。作为应用程序，我们计算了与R和C上的拓扑欧拉数，在P^n的完整交叉点上与D-planes的算术计数相关的Euler类。
We equate various Euler classes of algebraic vector bundles, including those of [BM, KW, DJK], and one suggested by M.J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class, and give formulas for local indices at isolated zeros, both in terms of 6-functor formalism of coherent sheaves and as an explicit recipe in commutative algebra of Scheja and Storch. As an application, we compute the Euler classes associated to arithmetic counts of d-planes on complete intersections in P^n in terms of topological Euler numbers over R and C.
