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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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