On the Hasse principle for Shimura curves
| dc.creator | Clark, Pete L. | |
| dc.date | 2005-10-12 | |
| dc.date | 2005-10-12 | |
| dc.date.accessioned | 2026-07-07T06:47:23Z | |
| dc.date.available | 2026-07-07T06:47:23Z | |
| dc.description | Let C be an algebraic curve defined over a number field K, of positive genus and without K-rational points. We conjecture that there exists some extension field L over which C violates the Hasse principle, i.e., has points everywhere locally but not globally. We show that our conjecture holds for all but finitely many Shimura curves of the form X^D_0(N)_{/Q} or X^D_1(N)_{/Q}, where D > 1 and N are coprime squarefree positive integers. The proof uses a variation on a theorem of Frey, a gonality bound of Abramovich, and an analysis of local points of small degree. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510239 | |
| dc.identifier | http://arxiv.org/abs/math/0510239 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103636 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | On the Hasse principle for Shimura curves | |
| dc.type | text |