The affine Deligne-Lusztig variety $X_{\mu}(b)$ is a certain locally closed subscheme of the affine Grassmannian. Recently, the $J_b$-action of top-dimensional irreducible components of $X_\mu(b)$ was determined quite explicitly, and it is also expected that $X_{\mu}(b)$ is equidimensional. Hartl and Viehmann already verified it in the equal characteristic case. In this talk, we show the equidimensionality in the mixed characteristic case.

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