Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein.
Infinite class field towers of quadratic fields.
Counting points on elliptic curves over finite fields
We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic polynomial...
Homophonic quotients of free groups. (Quotients homophones des groupes libres.)
Integral points of a modular curve of level 11
Computing Iwasawa modules of real quadratic number fields
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