Torsors on semistable curves and degenerations

In this paper, we answer two long-standing questions on the classification of G -torsors on curves for an almost simple, simply connected algebraic group G over the field of complex numbers. The first is the construction of a flat degeneration of the moduli of G -torsors on smooth projective curves...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2022-06, Vol.132 (1), Article 27
Main Author: Balaji, V
Format: Article
Language:English
Subjects:
Complex numbers
Degeneration
Mathematics
Mathematics and Statistics
Rings (mathematics)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we answer two long-standing questions on the classification of G -torsors on curves for an almost simple, simply connected algebraic group G over the field of complex numbers. The first is the construction of a flat degeneration of the moduli of G -torsors on smooth projective curves when the smooth curve degenerates to an irreducible nodal curve and the second one is to give an intrinsic definition of (semi)stability for a G -torsor on an irreducible projective nodal curve . A generalization of the classical Bruhat–Tits group schemes to two-dimensional regular local rings and an application of the geometric formulation of the McKay correspondence provide the key tools.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-021-00651-6