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

Original language | English (US) |
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Pages (from-to) | 485-500 |

Number of pages | 16 |

Journal | Algebra and Number Theory |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2 2019 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- Algebra and Number Theory