Resumen de On the local Langlands and Jacquet�Langlands correspondences

Guy Henniart

• Let F be a locally compact non Archimedean field, and D a division algebra with centre F and finite dimension d2 over F. Fix an integer r  1, and let G = GLn(F ), G = GLr(D), where n = rd. Smooth irreducible representations of G are related to those of G via the Jacquet�Langlands correspondence, whereas the Langlands correspondence relates such representations of G to degree n representations of the absolute Galois group of F. We review some recent results on those correspondences, in particular on their explicit description.