On pseudo-rotations of the annulus with generic rotation number

We show that for a Baire generic rotation number $\alpha \in \mathbb{R}\mathrm{/}\mathbb{Z}$, the set of area preserving $C^{\mathrm{\infty }}$-pseudo-rotations of the annulus $\mathbb{A}$ with rotation number $\alpha$ equals the closure of the set of area preserving $C^{\mathrm{\infty }}$-pseudo-rotations which are smoothly conjugate to the rotation $R_{\alpha }$. As a corollary, a $C^{\mathrm{\infty }}$-generic area preserving pseudo-rotation of the annulus with a Baire generic rotation number $\alpha$ is weakly mixing.