# Congruences of the cardinalities of rational points of log Fano varieties and log Calabi-Yau varieties over the log points of finite fields

## TL;DR

This paper establishes congruences for the number of rational points on log Fano and log Calabi-Yau varieties over finite fields, within the framework of log scheme theory, advancing understanding in arithmetic geometry.

## Contribution

It introduces congruences for rational point counts on log Fano and log Calabi-Yau varieties using log scheme theory, a novel approach in arithmetic geometry.

## Key findings

- Congruences for rational points over finite fields.
- Application of log scheme theory to algebraic varieties.
- Enhanced understanding of arithmetic properties of log varieties.

## Abstract

In this article we give the definitions of log Fano varieties and log Calabi-Yau varieties in the framework of theory of log schemes of Fontain-Illusie-Kato and give congruences of the cardinalities of rational points of them over the log points of finite fields.