Skip to main content
2 of 2
added 13 characters in body; edited title

Number of rational points over finite fields mod $q$ is birational invariant

I heard that if $\mathbf F_q$ is a finite field, $X, Y$ are birational smooth proper variety over $\mathbf F_q$, then $\#(X(\mathbf F_q)) \equiv \#(Y(\mathbf F_q)) \pmod q$, and I heard that the proof uses crystalline cohomology. Anyone could explain the proof, or is there a reference, thanks.