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- Title
Néron blowups and low-degree cohomological applications.
- Authors
Mayeux, Arnaud; Richarz, Timo; Romagny, Matthieu
- 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 0 (integral points) and degree 1 (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 g, and we show that many level structures on moduli stacks of G-bundles are encoded in torsors under Néron blowups of G.
- Subjects
BLOWING up (Algebraic geometry); MATHEMATICAL singularities; COHOMOLOGY theory; ISOMORPHISM (Mathematics); GROUP theory
- Publication
Algebraic Geometry, 2023, Vol 10, Issue 6, p729
- ISSN
2313-1691
- Publication type
Article
- DOI
10.14231/ag-2023-026