Hi,


Suppose that $E/F$ is a unramified extension of local fields of characteristic zero. Let
$G = GL\_n$. Then it is well-known (due to Clozel?) that base change of tempered representations from $G(F)$ to $G(E)$ holds.


Question: does the same result hold in the case of characteristic $p > 0$?


Thanks!


EDIT: As Olivier says, this actually seems to follow immediately from LLC for function fields.
Thanks!



unramified base change in characteristic p > 0?
Maybe I should reproduce my comment as an answer, in order for MO not to treat the question has unanswered.


The full local Langlands correspondence is a theorem of G.Laumon, M.Rappoport and U.Stuhler in $\mathcal D$-elliptic sheaves and the Langlands correspondence (Invent. Math. 113).


Here is the Mathscinet review:


<http://www.ams.org/mathscinet/search/publdoc.html?pg1=IID&s1=110755&vfpref=html&r=29&mx-pid=1228127>


The result for $n=2$ is due to Deligne. 


