Integral points on generic fibers
| Autor: | Arnaud Bodin |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Infinite number
Polynomial Mathematics - Number Theory General Mathematics Existential quantification Rational polynomial Automorphism Combinatorics Mathematics - Algebraic Geometry Bounded function FOS: Mathematics Number Theory (math.NT) Algebraic number Algebraic Geometry (math.AG) Value (mathematics) Mathematics |
| Zdroj: | Journal of the London Mathematical Society. 81:563-572 |
| ISSN: | 0024-6107 |
| DOI: | 10.1112/jlms/jdp084 |
| Popis: | Let P(x,y) be a rational polynomial and k in Q be a generic value. If the curve (P(x,y)=k) is irreducible and admits an infinite number of points whose coordinates are integers then there exist algebraic automorphisms that send P(x,y) to the polynomial x or to x^2-dy^2. Moreover for such curves (and others) we give a sharp bound for the number of integral points (x,y) with x and y bounded. 12 pages |
| Databáze: | OpenAIRE |
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