| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4586904 | Journal of Algebra | 2010 | 7 Pages |
Abstract
Pop proved that a smooth curve C over an ample field K with C(K)≠∅ has |K| many rational points. We strengthen this result by showing that there are |K| many rational points that do not lie in a given proper subfield, even after applying a rational map. This has several consequences. For example, we gain insight into the structure of existentially definable (i.e. diophantine) subsets of ample fields.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
