Witt vector affine Springer fibers

We establish dimension formulas for the Witt vector affine Springer fibers associated to a reductive group over a mixed characteristic local field, under the assumption that the group is essentially tamely ramified and the residue characteristic is not bad. Besides the discriminant valuations that show up in classical works on the usual affine Springer fibers, our formula also involves the Artin conductors and the Kottwitz invariants of the relevant conjugacy classes.