Residues on Affine Grassmannians

Résidus sur les grassmanniennes affines

Mathieu Florence (1) , Philippe Gille (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 ICJ - Institut Camille Jordan

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

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

Mathieu Florence, Philippe Gille. Residues on Affine Grassmannians. 2019. ⟨hal-02338391v1⟩