Journal of the Ramanujan Mathematical Society
Volume 31, Issue 2, June 2016 pp. 189–194.
Galois points on varieties
Authors:
Moshe Jarden and Bjorn Poonen
Author institution:School of Mathematics, Tel Aviv University Ramat Aviv, Tel Aviv 6139001, Israel
Summary:
A field K is ample if for every geometrically integral K-variety V
with a smooth K-point, V(K) is Zariski dense in V.
A field K is Galois-potent if every geometrically integral K-variety
has a closed point whose residue field is Galois over K.
We prove that every ample field is Galois-potent.
But we construct also non-ample Galois-potent fields;
in fact, every field has a regular extension with these properties.
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