Counting rational points on a Grassmannian

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.

arXiv commentFixed more minor errors, plus a proof for the counting formula on a flag variety