# Counting rational points on a Grassmannian

## TL;DR

This paper provides a refined estimate for counting rational points on Grassmannian varieties with bounded height, improving classical results and extending to all points, with implications for flag varieties.

## Contribution

It introduces a new counting formula for rational points on Grassmannians that counts all points, refining previous bounds and extending to flag varieties.

## Key findings

- Derived a comprehensive estimate for rational points on Grassmannians.
- Extended counting results to flag varieties.
- Improved upon classical bounds by including all points.

## Abstract

We prove an estimate on the number of rational points on the Grassmannian variety of bounded twisted height, refining the classical results of Schmidt ([12]) and Thunder ([20]) over the rational field: most importantly, our formula counts all points. Among the consequences are a couple of new implications on the classical subject of counting rational points on flag varieties.