Abstract: Let F/Q_p be a finite extension of the field of p-adic numbers. Let G be a reductive group (defined and split over O_F), let G^\vee be its dual group, let k be a field of characteristic p. Motivated by the (at present highly speculative) search for a p-modular local Langlands correspondence, we try to relate:
--- (supersingular) modules over the pro-p Iwahori Hecke k-algebra attached to G/F
--- G^\vee-valued Galois representations over k, i.e. homomorphisms Gal(\overline{F}/F) to G^{\vee}(k)