Matthew Emerton mentioned recently the relevance of Dwork's "p-adic cycles". As I wonder if I should read that, reviews of it are ambiguous, I'd be happy on remarks and possible further bibl. hints. ...
Using p-adic analysis, Dwork was the first to prove the rationality of the zeta function of a variety over a finite field. From what I have seen, in algebraic geometry, this method is not used much ...