let $p$ be a prime number and $ q_p$  the field  of $p$-adic numbers.

the representations of  a cousin of the galois group of an algebraic closure of $ q_p$ are related (the {\bf langlands's bridge}) to the representations of reductive $p$-adic groups, for instance $sl_2(q_p),  gl_n(q_p) $.   the irreducible representations $\pi$ of reductive $p$-adic groups are  easier  to study than those of the galois groups but they are rarely finite dimensional. their classification is very involved but their behaviour  around the identity, that we call the ``asymptotics'' of $\pi$, are expected to be more uniform. we shall survey what is known  (joint work with guy henniart), and what it suggests.

tba