Heegner Points on Cartan Non-split Curves
نویسندگان
چکیده
منابع مشابه
Heegner points on Mumford–Tate curves
1 Shimura curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 2 Heegner points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 3 The regulator term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 4 The conjecture . . . . . . . . . . . . . . ....
متن کاملHeights of Heegner Points on Shimura Curves
Introduction 2 1. Shimura curves 6 1.1. Modular interpretation 6 1.2. Integral models 13 1.3. Reductions of models 17 1.4. Hecke correspondences 18 1.5. Order R and its level structure 25 2. Heegner points 29 2.1. CM-points 29 2.2. Formal groups 34 2.3. Endomorphisms 37 2.4. Liftings of distinguished points 40 3. Modular forms and L-functions 43 3.1. Modular forms 44 3.2. Newforms on X 49 3.3. ...
متن کاملConstructing Rational Points on Elliptic Curves Using Heegner Points
These are the notes I wrote for my candidacy talk. The aims for this talk were to understand Heegner points, examine the different ways they can be characterized, and get an idea of how to construct rational points on an elliptic curve using Heegner points. I cite some good references at the end if you are also trying to begin learning about this beautiful topic. The goal of this talk is to exp...
متن کاملAutomorphism group of split Cartan modular curves
We determine the automorphism group of the split Cartan modular curves Xsplit(p) for all primes p.
متن کاملHigher Heegner points on elliptic curves over function fields
Let E be a modular elliptic curve defined over a rational function field k of odd characteristic. We construct a sequence of Heegner points on E, defined over a Zp -tower of finite extensions of k, and show that these Heegner points generate a group of infinite rank. This is a function field analogue of a result of C. Cornut and V. Vatsal.
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2016
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2015-047-6