NDLI: Independence of points on elliptic curves arising from special points on modular and Shimura curves, II: local results

Content Provider	Scilit
Author	Buium, Alexandru Poonen, Bjorn
Copyright Year	2009
Description	Journal: Compositio Mathematica In the predecessor to this article, we used global equidistribution theorems to prove that given a correspondence between a modular curve and an elliptic curveA, the intersection of any finite-rank subgroup ofAwith the set of CM-points ofAis finite. In this article we apply local methods, involving the theory of arithmetic differential equations, to provequantitativeversions of a similar statement. The new methods apply also to certain infinite-rank subgroups, as well as to the situation where the set of CM-points is replaced by certain isogeny classes of points on the modular curve. Finally, we prove Shimura-curve analogues of these results.
Ending Page	602
Starting Page	566
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x09004011
Journal	Compositio Mathematica
Issue Number	3
Volume Number	145
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2009-05-13
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Independence of points on elliptic curves arising from special points on modular and Shimura curves, II: local results