Title: Congruences and special values of L-functions

Abstract: Conjectures on special values of L-functions, like the Birch and Swinnerton-Dyer conjecture, predict the value of L-functions of elliptic curves, abelian varieties, modular forms and more generally motives at integers. In this talk, I discuss the following question: suppose two motives are congruent modulo a prime p and suppose we know conjectures on special values of L-functions are true for the first one, can we deduce that they are also true for the second one? I show that this is the case (under mild hypotheses) if the two motives come from eigencuspforms.