An arithmetic Bern\v{s}tein-Ku\v{s}nirenko inequality

Autor:	Martínez, César, Sombra, Martín
Rok vydání:	2016
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry Primary 14G40 Secondary 14C17 14M25 52A41
Druh dokumentu:	Working Paper
Popis:	We present an upper bound for the height of the isolated zeros in the torus of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions associated to the chosen height function and to the system of Laurent polynomials. We also show that this bound is close to optimal in some families of examples. This result is an arithmetic analogue of the classical Bern\v{s}tein-Ku\v{s}nirenko theorem. Its proof is based on arithmetic intersection theory on toric varieties. Comment: Revised version to appear in Mathematische Zeitschrift, 34 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1609.00509 Zobrazit plný text záznamu View this record from Arxiv