Generators of the pro-p Iwahori and Galois representations

Christophe Cornut (1) , Jishnu Ray (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

For an odd prime p, we determine a minimal set of topological generators of the pro-p Iwahori subgroup of a split reductive group G over Z_p. In the simple adjoint case and for any sufficiently large regular prime p, we also construct Galois extensions of Q with Galois group between the pro-p and the standard Iwahori subgroups of G.

Mots clés: Iwahori subgroup; Iwasawa theory

Domaines: Théorie des nombres [math.NT]; Théorie des groupes [math.GR]

Christophe Cornut, Jishnu Ray. Generators of the pro-p Iwahori and Galois representations. International Journal of Number Theory, 2018, 14 (1), ⟨10.1142/S1793042118500045⟩. ⟨hal-01398468⟩