What is the evidence for ice under the frozen carbon dioxide in Martian craters?
There are various different kinds of evidence. Measurements of infrared spectra by Mars Express show characteristic signatures of water in the polar caps, seen through the carbon dioxide layer. Other evidence for subsurface water on Mars comes from the Mars Odyssey mission. This spacecraft contained an instrument that was able to detect neutrons coming from the surface of Mars. Neutrons are emitted when cosmic rays (high energy particles from space) hit the surface of the planet; but hydrogen captures neutrons. So, if you see fewer neutrons than expected, there must be a large concentration of hydrogen compounds, most likely water. The Mars Odyssey measurements showed that there is a lot of hydrogen (and therefore likely water) near the poles (and in a few other places too). Since we know (from spectra and other information) that the surface ice is carbon dioxide, this water must be underneath the carbon dioxide.