Jacobiens, jacobiennes et stabilit\'e num\'erique

This paper is concerned with the complexity and stability of arithmetic operations in the jacobian variety of curves over the field of complex numbers, as the genus grows to infinity. We focus on modular curves. Efficient and stable computation in the jacobian of modular curves is useful for computing coefficients of modular forms in deterministic polynomial time. This work is part of my contribution to Edixhoven's program for solving this problem.