论文标题
Néron爆炸和低度的共同体应用
Néron blowups and low-degree cohomological applications
论文作者
论文摘要
我们定义了一般方案的扩张并研究其基本特性。在有利的情况下，小组计划的扩张再次被称为Néron爆炸。 We give two applications to their cohomology in degree zero (integral points) and degree one (torsors): we prove a canonical Moy-Prasad isomorphism that identifies the graded pieces in the congruent filtration of $G$ with the graded pieces in its Lie algebra $\mathfrak g$, and we show that many level structures on moduli stacks of $G$-bundles are encoded in torsors在$ g $的Néron爆炸下。
We define dilatations of general schemes and study their basic properties. Dilatations of group schemes are -- in favorable cases -- again group schemes, called Néron blowups. We give two applications to their cohomology in degree zero (integral points) and degree one (torsors): we prove a canonical Moy-Prasad isomorphism that identifies the graded pieces in the congruent filtration of $G$ with the graded pieces in its Lie algebra $\mathfrak g$, and we show that many level structures on moduli stacks of $G$-bundles are encoded in torsors under Néron blowups of $G$.
