Residues on Affine Grassmannians

Résidus sur les grassmanniennes affines

Mathieu Florence (1) , Philippe Gille (2, 3)

1 IMJ - Institut de Mathématiques de Jussieu
2 ICJ - Institut Camille Jordan
3 AGL - Algèbre, géométrie, logique

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.

Mots clés: affine grassmannians MSC 2000: 14M15; residues; affine grassmannians.; Group schemes; 20G35; affine grassmannians. MSC 2000: 14M15

Domaines: Géométrie algébrique [math.AG]; Théorie des groupes [math.GR]

Mathieu Florence, Philippe Gille. Residues on Affine Grassmannians. Journal für die reine und angewandte Mathematik, 2021, ⟨10.1515/crelle-2021-0007⟩. ⟨hal-02338391v4⟩