bei Google ScholarTitelangaben
Stoll, Michael:
Finite descent obstructions and rational points on curves.
In: Algebra & Number Theory.
Bd. 1
(2007)
Heft 4
.
- S. 349-391.
ISSN 1937-0652
DOI: https://doi.org/10.2140/ant.2007.1.349
Abstract
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 (k, A) has no nontrivial divisible element, then the information coming from finite abelian descent cuts out precisely the rational points of C. We conjecture that this is the case for all curves of genus at least 2. 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
finite abelian descent. Our conjecture therefore implies that the Brauer-Manin obstruction against rational points is the only one on curves.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Keywords: | rational point; descent obstruction; covering; twist; torsor under finite group scheme; Brauer-Manin obstruction |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra) Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra) > Lehrstuhl Mathematik II (Computeralgebra) - Univ.-Prof. Dr. Michael Stoll Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut |
| Titel an der UBT entstanden: | Nein |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 02 Feb 2015 15:47 |
| Letzte Änderung: | 02 Feb 2015 15:47 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/6220 |