  This article is devoted to studying the ramification of Galois torsors and of
$\ell$-adic sheaves in characteristic $p>0$ (with $\ell\not=p$). Let $k$ be a
perfect field of characteristic $p>0$, $X$ be a smooth, separated and
quasi-compact $k$-scheme, $D$ be a simple normal crossing divisor on $X$,
$U=X-D$, $\Lambda$ be a finite local ${\mathbb Z}_\ell$-algebra, $F$ be a
locally constant constructible sheaf of $\Lambda$-modules on $U$. We introduce
a boundedness condition on the ramification of $F$ along $D$, and study its
main properties, in particular, some specialization properties that lead to the
fundamental notion of cleanliness and to the definition of the characteristic
cycle of $F$. The cleanliness condition extends the one introduced by Kato for
rank one sheaves. Roughly speaking, it means that the ramification of $F$ along
$D$ is controlled by its ramification at the generic points of $D$. Under this
condition, we propose a conjectural Riemann-Roch type formula for $F$. Some
cases of this formula have been previously proved by Kato and by the second
author (T.S.).
