On rational singularities and counting points of schemes over finite rings

We study the connection between the singularities of a finite type Z-scheme X and the asymptotic point count of X over various finite rings. In particular, if the generic fiber X-Q = X x (SpecZ) Spec Q is a local complete intersection, we show that the boundedness of vertical bar X(Z/p(n)Z)vertical bar/p(ndimXQ) in p and n is in fact equivalent to the condition that X-Q is reduced and has rational singularities. This paper completes a recent result of Aizenbud and Avni.