Semi-simple groups that are quasi-split over a tamely-ramified extension

Philippe Gille (1)

1 AGL - Algèbre, géométrie, logique

Let K be a discretly henselian field whose residue field is separably closed. Answering a question raised by G. Prasad, we show that a semisimple K– group G is quasi-split if and only if it quasi–splits after a finite tamely ramified extension of K.

Mots clés: Galois cohomology; Linear algebraic groups; Bruhat-Tits theory

Domaines: Anneaux et algèbres [math.RA]; Théorie des nombres [math.NT]; Théorie des groupes [math.GR]

Philippe Gille. Semi-simple groups that are quasi-split over a tamely-ramified extension. Rendiconti del Seminario Matematico della Università di Padova, 2018, 140, pp.173-183. ⟨10.4171/RSMUP/7⟩. ⟨hal-01558507⟩