Let p be an odd prime. Let F be a p-adic field of residue cardinality q and let Z be the center of the mod p pro-p-Iwahori-Hecke algebra of the p-adic group GL_2(F). In this talk we define a scheme which parametrizes the semisimple mod p two-dimensional representations of the absolute Galois group of F. We explain its basic properties and then relate it to Spec Z. If time permits, we discuss some first applications. This is joint work with C. Pépin.