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.
Original language | English |
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Pages (from-to) | 189-194 |
Number of pages | 6 |
Journal | Journal of the Ramanujan Mathematical Society |
Volume | 31 |
Issue number | 2 |
State | Published - Jun 2016 |
Funding
Funders | Funder number |
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National Science Foundation | DMS-1069236 |
Simons Foundation | 340694 |
Minerva Foundation |