International Congress of Mathematicians

586 Michael Harriscorresponding to r is then the unique subquotient n(r) = ,E(fl'));£(s,0-n,E(n) ®0-n',E(fl'j) = JJ £ v (s, (T n>E (YY) ® CT„',£;(II'), tp v )is the product of local Deligne-Langlands e factors.VHere " denotes contragredient. The local additive characters tp v are assumedto be the local components of a continuous character of AE/E.1.6. The map a = a n: F'• Ao(n,F)^-Q(n,F)(i) takes values in Qo(n,F);(ii) defines a bijection Ao(n,F) ^> Qo(n,F);(iii) satisfies the remaining requirements of a local Langlands correspondence,especially (0.4)-The main burden of [LRS] is the construction of a class A sood (n, E) largeenough to satisfy (1.4): now a moot point, since Lafforgue has proved that all cuspidalautomorphic representations of GL(n) of a function field are "good" in thissense. The A sood (n, E) in [LRS] are the automorphic representations that contributeto the cohomology of an appropriate Drinfeld modular variety, constructedfrom scratch for the occasion, attached to the multiplicative group of a divisionalgebra of dimension n 2 over E, unramified at the chosen tv. Property (1.5) in this