Finite descent obstructions and rational points on curves
نویسندگان
چکیده
منابع مشابه
Finite Descent Obstructions and Rational Points on Curves
Let k be a number field and X a smooth projective k-variety. In this paper, we study the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points on X within the adelic points. Our main result is that if a curve C/k maps nontrivially into an abelian variety A/k such that A(k) is finite and X(k, A) has no nontrivial divisible elements,...
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Let k be a number field and X a smooth projective k-variety. In this paper, we discuss the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points on X within the adelic points. We relate finite descent obstructions to the Brauer-Manin obstruction; in particular, we prove that on curves, the Brauer set equals the set cut out by finit...
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In this paper, we discuss the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points within the adelic points on a smooth projective k-variety X , where k is a number field. When X is a curve of genus ≥ 2, we conjecture that the information coming from “finite abelian descent” cuts out precisely the rational points; we provide theor...
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Let k be a number field and X a smooth projective k-variety. In this paper, we discuss the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points on X within the adelic points. We relate finite descent obstructions to the Brauer-Manin obstruction; in particular, we prove that on curves, the Brauer set equals the set cut out by finit...
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Preface These notes treat the problem of counting the number of rational points on a curve defined over a finite field. The notes are an extended version of an earlier set of notes Aritmetisk Algebraisk Geometri – Kurver by Johan P. Hansen [Han] on the same subject. In Chapter 1 we summarize the basic notions of algebraic geometry, especially rational points and the Riemann-Roch theorem. For th...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2007
ISSN: 1937-0652
DOI: 10.2140/ant.2007.1.349