Department of Mathematics, Faculty of Science, Okayama University
Doi
Abstract
The block approximation theorem is an extensive general-
ization of both the well known weak approximation theorem from valu-
ation theory and the density property of global fields in their henseliza-
tions. It guarantees the existence of rational points of smooth affine
varieties that solve approximation problems of local-global type (see
e.g. [HJP07]). The theorem holds for pseudo real closed fields, by
[FHV94]. In this paper we prove the block approximation for pseudo-F-
closed fields K, where F is an ´etale compact family of valuations of K
with bounded residue fields (Theorem 4.1). This includes in particular
the case of pseudo p-adically closed fields and generalizations of these
like the ones considered in [HJP05]