On rational singularities and counting points of schemes over finite rings

Itay Glazer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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 = X xSpecℤ Specℚ is a local complete intersection, we show that the boundedness of |X(ℤ/p n ℤ)|/p ndimX 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.

Original languageEnglish (US)
Pages (from-to)485-500
Number of pages16
JournalAlgebra and Number Theory
Volume13
Issue number2
DOIs
StatePublished - Mar 2 2019
Externally publishedYes

Keywords

  • Analysis on p-adic varieties
  • Asymptotic point count
  • Complete intersection
  • Rational singularities

ASJC Scopus subject areas

  • Algebra and Number Theory

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