Vol. 13, No. 2, 2019

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On rational singularities and counting points of schemes over finite rings

Itay Glazer

Vol. 13 (2019), No. 2, 485–500

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

rational singularities, complete intersection, analysis on p-adic varieties, asymptotic point count
Mathematical Subject Classification 2010
Primary: 14B05
Secondary: 14G05
Received: 3 March 2018
Revised: 27 August 2018
Accepted: 24 December 2018
Published: 2 March 2019
Itay Glazer
Faculty of Mathematics and Computer Science
Weizmann Institute of Science
Rehovot 7610001