MAT 1210 (Arithmetic of Elliptic Curves);
Main reference: Silverman's book
Homework 1 (due Feb 25):
Problems 1.10, 2.3, 2.4, 3.3(d) + show this is an elliptic curve + find a Weierstrass equation (hint: recall how we found Weierstrass coordinates for a general elliptic curves), 3.5, 3.8
Consider E: y^2 = x^3 - 43x + 166 over the rationals and P = (3,8). Show by hand that P has finite order. (Hint: it may be more
efficient to compute some 2^i P first.)
Adequate subgroups
(with Robert Guralnick,
Richard Taylor, and
Jack Thorne).
Appendix to On the automorphy of l-adic Galois representations with small residual image by Jack Thorne.
Journal de l'Institut de Mathématiques de Jussieu 11 (2012), no. 4, 907-920.
p-modular representations of p-adic groups
Notes for my minicourse at IMS Singapore, April 2013 (typed by Karol Koziol). These notes focus on GL_{2}(Q_{p}).
Appeared in IMS Lecture Notes Series, vol. 30 (2015).