Base Change For Mod P Representations Of P-adic General Linear Groups

This thesis considers the base change problem for mod p representations of gen-eral linear groups over p-adic fields.We first give the definition of base change over an unramified extension and show that it is compatible with the classification theorem for irreducible admissible mod p representations of GL?n?.The construction of the base change are discussed for generalized Steinberg representations of GL?n?and supersin-gular representations of GL₂?Q_p?.