Being rather surprised, I decided to look at reviews of Carrier's books. The first one I came upon is here:
Christina Petterson, (December 2015). "On the Historicity of Jesus: Why We Might Have Reason for Doubt". Relegere: Studies in Religion and Reception. 5 (2): 253–258.
It has argued for a long time that Jesus is a historical person who was made into a mythical celestial being. Paul is often cited as the culprit. I'm ok with those arguments, though I strenuously disagree . But there is no historical evidence at all is a proposition that cannot be intelligently argued, given the enormous scholarship over the past 2000 years. From reading Carrier's blog, he seems to think he's the only one who ever came up with his hypothesis, all others being ignorant or liars.
Paul did assert that Jesus' death was "an earthly occurence." The aftermath, on the other hand...