On rationally connected varieties over C1 fields of characteristic 0

Diophantine problems over tamely ramified fields

“…(i) Hogadi-Xu use proper varieties rather than projective varieties but this does not make a difference in view of Chow's lemma. (ii) If k is geometrically C 1 and large of characteristic 0, then every rationally connected k-variety (not necessarily smooth or proper) has a k-point (see Lemma 3.2 [Pie22]).…”

“…This is, in a way, complementary to Lang's theorem [Lan52] which says that the maximal unramified extension of any non-archimedean local field is C 1 . We note that it is a prominent open problem whether Q ur p is geometrically C 1 ; see [ELW15,DK17,Pie22] for partial results in this direction.…”