Fabien Morel

Abstract:   In this talk I will first recall the statement of the Friedlander-Milnor conjecture on the cohomology of algebraic groups and give (new) examples in low degrees. After briefly recalling the Theorem of Suslin establishing this conjecture for the infinite linear group GL, I will sketch a new approach which relies on basic results in A1-homotopy theory (Hurewicz theorem, Lower central series spectral sequence, A1-coverings,...) which allows us to prove the conjecture for semi-simple groups of small ranks, like SL_2 and SL_3.