A note on an anabelian open basis for a smooth variety

Abstract

Schmidt and Stix proved that every smooth variety over a field finitely generated over the field of rational numbers has an open basis for the Zariski topology consisting of “anabelian” varieties. This was predicted by Grothendieck in his letter to Faltings. In the present paper, we generalize this result to smooth varieties over generalized sub-$p$-adic fields. Moreover, we also discuss an absolute version of this result.