Schinzel Hypothesis on average and rational points
نویسندگان
چکیده
Abstract We resolve Schinzel’s Hypothesis (H) for $$100\%$$ 100 % of polynomials arbitrary degrees. deduce that a positive proportion diagonal conic bundles over $${\mathbb {Q}}$$ Q with any given number degenerate fibres have rational point, and obtain similar results generalised Châtelet equations.
منابع مشابه
Rational Points on Curves
This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009. We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve C over Q. The focus is on practical aspects of this problem in the case that the genus of C is at least 2, and therefore the set of rat...
متن کاملRational points on curves
2 Faltings’ theorem 15 2.1 Prelude: the Shafarevich problem . . . . . . . . . . . . . . . . 15 2.2 First reduction: the Kodaira–Parshin trick . . . . . . . . . . . 17 2.3 Second reduction: passing to the jacobian . . . . . . . . . . . 19 2.4 Third reduction: passing to isogeny classes . . . . . . . . . . . 19 2.5 Fourth reduction: from isogeny classes to `-adic representations 21 2.6 The isogen...
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 2022
ISSN: ['0020-9910', '1432-1297']
DOI: https://doi.org/10.1007/s00222-022-01153-6