Canonical height functions for monomial maps (Q2867003)

A height function is said to satisfy the Northcott finiteness property if for every positive real number \(B\), the set of rational points of height at most \(B\) is finite. The purpose of the paper under review is to prove that the Northcott finiteness property -- which is known not to hold for Silverman's canonical height associated to general dominant rational endomorphisms of projective space -- is satisfied by Silverman's canonical height (see \textit{J. H. Silverman} [Invent. Math. 105, No. 2, 347--373 (1991; Zbl 0754.14023)]) under certain conditions. The authors then define what they call the total canonical height, and prove that it satisfies a uniqueness property and the Northcott finiteness property for certain classes of maps defined by monomials.