  Statistical comparisons of microwave maps in the GHz range and X-ray maps at
around 1 keV are an interesting probe to constrain different astrophysical
phenomena. Possible correlations on various angular scales and with different
frequency (energy) dependences, although not expected at present day
experimental sensitivity, could in principle be due to Galactic
emission/absorption, the Sunyaev-Zel'dovich effect, the Integrated Sachs-Wolfe
effect in cosmological models with a cosmological constant or low density, or
X-ray luminous radio sources such as radio-loud AGNs. I report on work
cross-correlating the COBE DMR and ROSAT All-Sky Survey in a selected area of
the sky. This area (+40 deg < b, 70 deg < l < 250 deg) is the best presently
available data set probing the medium-hard extragalactic X-ray background
around 1 keV. No significant correlation on astrophysically relevant scales has
been found in this analysis, but it will be possible to infer constraints from
the limits.
