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Independence of points on elliptic curves arising from special points on modular and Shimura curves, II: local results
| Content Provider | Semantic Scholar |
|---|---|
| Author | Buium, Alexandru Poonen, Bjorn |
| Copyright Year | 2009 |
| Abstract | In the predecessor to this article, we used global equidistribution theorems to prove that given a correspondence between a modular curve and an elliptic curve A, the intersection of any finite-rank subgroup of A with the set of CM-points of A is finite. In this article we apply local methods, involving the theory of arithmetic differential equations, to prove quantitative versions of a similar statement. The new methods apply also to certain infinite-rank subgroups, as well as to the situation where the set of CMpoints is replaced by certain isogeny classes of points on the modular curve. Finally, we prove Shimura-curve analogues of these results. |
| Starting Page | 566 |
| Ending Page | 602 |
| Page Count | 37 |
| File Format | PDF HTM / HTML |
| DOI | 10.1112/S0010437X09004011 |
| Volume Number | 145 |
| Alternate Webpage(s) | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/451893B556EEEFF4572B1CB30E4A0CB9/S0010437X09004011a.pdf/independence_of_points_on_elliptic_curves_arising_from_special_points_on_modular_and_shimura_curves_ii_local_results.pdf |
| Alternate Webpage(s) | https://doi.org/10.1112/S0010437X09004011 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
