  Let k be a p-adic field. Some time ago, D. Harbater [9] proved that any
finite group G may be realized as a regular Galois group over the rational
function field in one variable k(t), namely there exists a finite field
extension $F/k(t)$, Galois with group G, such that F is a regular extension of
k (i.e. k is algebraically closed in F). Moreover, one may arrange that a given
k-place of k(t) be totally split in F. Harbater proved this theorem for k an
arbitrary complete valued field. Rather formal arguments ([10, \S 4.5]; \S2
hereafter) then imply that the theorem holds over any `large' field k. This in
turn is a special case of a result of Pop [15], hence will be referred to as
the Harbater/Pop theorem. We refer to [10], [16], [6] for precise references to
the literature (work of D\`ebes, Deschamps, Fried, Haran, Harbater, Jarden,
Liu, Pop, Serre, and V\"olklein).
  Most proofs (see [10], [19, 8.4.4, p.~93] and Liu's contribution to [16]; see
however [15]) first use direct arguments to establish the theorem when G is a
cyclic group (here the nature of the ground field is irrelevant), then proceed
by patching, using either formal or rigid geometry, together with GAGA
theorems.
  In the present paper, where I take the case of algebraically closed fields
for granted, I show how a technique recently developed by Koll\'ar [12] may be
used to give a quite different proof of the Harbater/Pop theorem, when the
`large' field k has characteristic zero. This proof actually gives more than
the original result (see comment after statement of Theorem 1).
