Event Details

Unramified Langlands Correspondence for Tori

In the beginning of the 70's, R. Langlands described the space of continuous automorphic characters of an algebraic torus T, defined over a global field F and splitting over a Galois extension E, in terms of the group of continuous, first-cohomology classes of the relative Weil group of E/F with values in the complex dual torus. In some sense, this correspondence launched what is now known as the Langlands programme, which has been a fruitful area of research since then. In this talk, we show that, when topologized in the sense of C. Moore, the cohomology group above is a metric space and its identity component parametrizes the space of unramified characters. This is an ongoing joint work with E. Opdam.