We study the connection between the singularities of a finite type -scheme and the asymptotic point count of over various finite rings. In particular, if the generic fiber is a local complete intersection, we show that the boundedness of in and is in fact equivalent to the condition that is reduced and has rational singularities. This paper completes a recent result of Aizenbud and Avni.
"On rational singularities and counting points of schemes over finite rings." Algebra Number Theory 13 (2) 485 - 500, 2019. https://doi.org/10.2140/ant.2019.13.485