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2019 On rational singularities and counting points of schemes over finite rings
Itay Glazer
Algebra Number Theory 13(2): 485-500 (2019). DOI: 10.2140/ant.2019.13.485

Abstract

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 dimX 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.

Citation

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Itay Glazer. "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

Information

Received: 3 March 2018; Revised: 27 August 2018; Accepted: 24 December 2018; Published: 2019
First available in Project Euclid: 26 March 2019

zbMATH: 07042066
MathSciNet: MR3927053
Digital Object Identifier: 10.2140/ant.2019.13.485

Subjects:
Primary: 14B05
Secondary: 14G05

Keywords: analysis on p-adic varieties , asymptotic point count , complete intersection , rational singularities

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2019
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