• big Heegner points
• Birch and Swinnerton-Dyer conjecture
• elliptic curves
• Heegner points
• Hida families

In this thesis, we present the main ingredient that was used by Kolyvagin and Gross-Zagier to prove the most important case of the Birch and Swinnerton-Dyer conjecture. These are Heegner points and Kolyvagin systems. Heegner points are points defined on rational elliptic curves over an imaginary quadratic field K satisfying certain hypotheses. On the other hand, Kolyvagin systems are collections of compatible cohomology classes in the Galois cohomology of quotients of the Tate module of the elliptic curve. Kolyvagin defined a Kolyvagin system from Heegner points.

We also generalize this machinery to the p-adic setting. To do that, we first define \Lambda-adic forms that are q-expansions with coefficients in a power series ring \Lambda=O[[X]], where O is an integral extension of Z_p. \Lambda-adic forms interpolate p-adically a family of modular forms. Then, we associate the big Galois representation to a \Lambda-adic form. Finally, we define big Heegner points that are 1-cocycles for the cohomology of a big Galois representation. These classes give back elements of the Kolyvagin system defined from Heegner points when specialised at modular forms of weight 2.