Help me find reliable sources on the prevalence of women lying about being raped?

On one newspaper forum I frequent there is a semi-trollish poster who likes to throw out the “fact” that women are giant rapists and that we routinely lie about being raped.

I have tried to find good sources to debunk this guy but all the statistics I am finding tend to be buried in articles where they don’t cite their sources. I am also being buried under links to sites where some people are big believers in this claptrap.

Does anyone here have easy access to any studies that have been done that speak to this?