  We introduce a quotient of the Grothendieck ring of varieties by identifying
classes of universally homeomorphic varieties. We show that the standard
realization morphisms factor through this quotient, and we argue that it is the
correct value ring for the theory of motivic integration on formal schemes and
rigid varieties in mixed characteristic. The present note is an excerpt of a
detailed survey paper which will be published in the proceedings of the
conference "Motivic integration and its interactions with model theory and
non-archimedean geometry" (ICMS, 2008).
