Local triviality for G-torsors

Philippe Gille (1) , Raman Parimala , V Suresh

1 AGL - Algèbre, géométrie, logique

Let C → Spec(R) be a relative proper flat curve over an henselian base. Let G be a reductive C-group scheme. Under mild technical assumptions, we show that a G-torsor over C which is trivial on the closed fiber of C is locally trivial for the Zariski topology.

Mots clés: deformation; Reductive group scheme; torsor

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Philippe Gille, Raman Parimala, V Suresh. Local triviality for G-torsors. 2019. ⟨hal-01978093v2⟩