MATH Seminar
| Title: The set of non-n-th powers in a number field is Diophantine |
|---|
| Seminar: Algebra |
| Speaker: Jean-Louis Colliot-Thelene of Universite Paris-Sud |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2014-05-08 at 3:00PM |
| Venue: W306 |
| Download Flyer |
| Abstract: In a joint work with J. Van Geel, we prove: For any natural integer n, the complement of the set of n-th powers in a number field k is the image of the set of k-rational points of some k-variety X under some k-morphism from X to the affine line. For n=2, this is a result of B. Poonen (2009). His proof uses local-global theorems (CT, Coray, Sansuc, 1980) for rational points on Ch\^{a}telet surfaces. Our proof for n arbitrary combines Poonen’s method and local-global theorems (CT, Swinnerton-Dyer, Skorobogatov, 1994, 1998) for zero-cycles on higher dimensional analogues of Ch\^{a}telet surfaces. |
See All Seminars