Teissier's problem on inequalities of nef divisors over an arbitrary field

Abstract

Boucksom, Favre and Jonsson establish in [4] an analog of Diskant's inequality in convex geometry for nef and big line bundles on a complete algebraic variety over an algebraically closed field of characteristic zero (Theorem F [4]), from which they deduce a solution (Theorem D [4]) to a problem of Teissier (Problem B [29]) on proportionality of nef divisors. In this paper we extend these results to a complete variety over an arbitrary field k.