Journal of the Ramanujan Mathematical Society

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Galois Points on Varieties


Affiliations
1 School of Mathematics, Tel Aviv University Ramat Aviv, Tel Aviv-6139001, Israel
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA-02139-4307, United States
     

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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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  • Galois Points on Varieties

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Authors

Moshe Jarden
School of Mathematics, Tel Aviv University Ramat Aviv, Tel Aviv-6139001, Israel
Bjorn Poonen
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA-02139-4307, United States

Abstract


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.