  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.
