N\'eron blowups and low-degree cohomological applications
Algebraic Geometry
2020-03-16 v4
Abstract
We define dilatations of general schemes and study their basic properties. Dilatations of group schemes are -- in favorable cases -- again group schemes, called N\'eron 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 with the graded pieces in its Lie algebra , and we show that many level structures on moduli stacks of -bundles are encoded in torsors under N\'eron blowups of .
Cite
@article{arxiv.2001.03597,
title = {N\'eron blowups and low-degree cohomological applications},
author = {Arnaud Mayeux and Timo Richarz and Matthieu Romagny},
journal= {arXiv preprint arXiv:2001.03597},
year = {2020}
}
Comments
This 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