Néron blowups and low-degree cohomological applications

Abstract

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 $G$.

arXiv commentThis is the joint work of two earlier works on dilatations, conducted around the same time independently by the authors. This new version includes minor corrections

References in corpus (4)

• The intersection motive of the moduli stack of shtukas
• Local Models For The Moduli Stacks of Global $G$-Shtukas
• Functoriality of Moduli Spaces of Global $\mathbb{G}$-Shtukas
• Fibration de Hitchin et endoscopie

Cited by in corpus (1)

• Harder-Narasimhan stratification for the moduli stack of parabolic vector bundles