Sur la conjecture de remmert

This paper is a survey of the main works on the so-called Remmert's conjecture, if Xⁿ is a closed, homogeneous complex manifold with automorphism group Aut(X) then dim(Aut(X) ≤ n² + 2n. We describe the structure of a closed, homogeneous complex manifold X, prove Remmert's conjecture for Kähler homogeneous manifolds, then describe the counterexamples constructed by Snow and Winkelman with dim(X) = 3m + 1 and dim(Aut(X) = 3^m + 3m, and finally show Akhiezer's theorem (which gives a bound on dim(Au(X)) for fixed n, being thus a weak version of Remmert's conjecture).