We describe the context of the question and remind some well known properties of fθ = e 2iπθz + z2. Then we list the ingredients of the proof by A. Cheritat and X. Buff of the existence of a θ Cremer with m(Kθ) > 0 : Mc Mullen’s density theorem; preservation of half the area of the Siegel disc (JSPM 3); upper semi continuity of the Siegel disc (JSPM 2), which relies on a renormalization property (JSPM 1). Finally we give a brief sketch of the final proof, which shall be developed in JSPM 4 .