A lisse sheaf, in the usual finite-rank 
-adic sense, is an adic sheaf whose
finite-level reductions are locally constant. More precisely, let 
be a prime number, let 
be a finite
extension of the l-adic numbers 
, and let 
be its valuation ring,
with uniformizer 
. On an algebraic variety 
over a field
of characteristic different from 
, a lisse 
-sheaf of rank 
is represented by a compatible system 
of locally constant étale sheaves
of free modules of rank 
over 
, with reduction isomorphisms
 |
Inverting 
gives a lisse 
-sheaf
(Milne 2013, pp. 124-126).
For a connected normal variety 
,
choose a geometric basepoint, that is, a point of 
valued in a separably closed field.
Such a field has no proper finite separable
extension. This choice identifies lisse 
-sheaves with finite-dimensional continuous group representations of its étale
fundamental group over 
(Kedlaya 2019, §15.2). The local constancy of the finite reductions does not
require the entire adic object to become constant after pullback along a finite surjective étale
morphism.
