When does an affine curve have an algebraic integer point?

Autor:	B. J. Birch
Rok vydání:	1985
Předmět:	Combinatorics Discrete mathematics Stable curve General Mathematics Integer points in convex polyhedra Dimension of an algebraic variety Algebraic curve Algebraic integer Algebraic number field Affine variety Mathematics Singular point of an algebraic variety
Zdroj:	Glasgow Mathematical Journal. 27:1-4
ISSN:	1469-509X 0017-0895
DOI:	10.1017/s0017089500006017
Popis:	The purpose of this note is to draw attention to the question in the title. If C⊆Kn is an (absolutely) irreducible affine curve, defined by equations over a number field K, an algebraic integer point of C is a point P = (x1, …, xn) with all of x1, …, xn integers of some finite extension L of K. For such an algebraic integer point P to exist, there are obviously necessary local conditions: for every prime p of K there must exist a prime B above p and a corresponding finite extension LB of the completion Kp such that C has a B-adic integer point. We would like to know whether these obviously necessary local conditions are also sufficient.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::fa0f2987bb450641377f9876b45c5af8 https://doi.org/10.1017/s0017089500006017 Zobrazit plný text záznamu