Séminaires à venir

As is well known, acts on the upper half plane . This space parametrizes elliptic curves (with extra data) which play a central role in a lot of mathematics (no knowledge of them is required). For technical reasons, it is sometimes preferable to replace with its quotient under the subgroup of matrices congruent to the identity mod (nevermind why). Now parametrizes elliptic curves with some other extra data, and the fact that the quotient map is surjective makes the extra data easier to grasp. In fact the situation generalizes, and begs the question: given a "matrix group" , when is surjective ? I will first give an elementary proof for , and then take this opportunity to give a quick introduction to algebraic groups so as to make sense of and in general. I will then give examples of when surjectivity holds or fails, and end the presentation on a criterion which provides an answer in a lot of cases.