An inequality in the theory of arithmetic on algebraic varieties

1949/10/01 by D. G. Northcott · 2 citations

paper · doi:10.1017/s0305004100025202

Abstract

The inequality which is proved here was established under different conditions in a paper entitled ‘Periodic points on an algebraic variety', which is to appear in the Annals of Mathematics . It is hoped that the new formulation will be more useful for applications. The present investigations use the rather sophisticated techniques of the ‘Theory of distributions’ which was developed by Weil (1). As the content of this theory may be unfamiliar to the reader, Weil's results are described at some length, though of course, his proofs are not given. The one result which we need and which is not given explicitly by Weil, is proved in detail.

Cited by

• A p-adic criterion for Lehmer's conjecture
• Singular intersections in families of abelian varieties

Related

• Moduli theory and arithmetic of algebraic varieties
• Inequalities for semistable families of arithmetic varieties
• Discrepancy of rational points in simple algebraic groups
• An application of the value distribution theory for semi-abelian varieties to problems of Ax-Lindemann and Manin-Mumford types
• Algebraic integers with conjugates in a prescribed distribution