Residues on Affine Grassmannians
Algebraic Geometry
2021-02-09 v3 Group Theory
Abstract
Given a linear group G over a field k, we define a notion of index and residue of an element g of G(k((t)). This provides an alternative proof of Gabber's theorem stating that G has no subgroups isomorphic to the additive or the commutative group iff G(k[[t]])= G(k((t))). In the case of a reductive group, we offer an explicit connection with the theory of affine grassmannians.
Cite
@article{arxiv.1910.14509,
title = {Residues on Affine Grassmannians},
author = {Mathieu Florence and Philippe Gille},
journal= {arXiv preprint arXiv:1910.14509},
year = {2021}
}