The Brauer–Manin obstruction for curves having split Jacobians
Samir Siksek[1]
- [1] Department of Mathematics and Statistics Faculty of Science Sultan Qaboos University P.O. Box 36 Al-Khod 123, Oman
Journal de Théorie des Nombres de Bordeaux (2004)
- Volume: 16, Issue: 3, page 773-777
- ISSN: 1246-7405
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topSiksek, Samir. "The Brauer–Manin obstruction for curves having split Jacobians." Journal de Théorie des Nombres de Bordeaux 16.3 (2004): 773-777. <http://eudml.org/doc/249265>.
@article{Siksek2004,
abstract = {Let $X \rightarrow \{\mathcal\{A\}\}$ be a non-constant morphism from a curve $X$ to an abelian variety $\{\mathcal\{A\}\}$, all defined over a number field $k$. Suppose that $X$ is a counterexample to the Hasse principle. We give sufficient conditions for the failure of the Hasse principle on $X$ to be accounted for by the Brauer–Manin obstruction. These sufficiency conditions are slightly stronger than assuming that $\{\mathcal\{A\}\}(k)$ and $\{\cyrX\}(\{\mathcal\{A\}\}/k)$ are finite.},
affiliation = {Department of Mathematics and Statistics Faculty of Science Sultan Qaboos University P.O. Box 36 Al-Khod 123, Oman},
author = {Siksek, Samir},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {3},
pages = {773-777},
publisher = {Université Bordeaux 1},
title = {The Brauer–Manin obstruction for curves having split Jacobians},
url = {http://eudml.org/doc/249265},
volume = {16},
year = {2004},
}
TY - JOUR
AU - Siksek, Samir
TI - The Brauer–Manin obstruction for curves having split Jacobians
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 3
SP - 773
EP - 777
AB - Let $X \rightarrow {\mathcal{A}}$ be a non-constant morphism from a curve $X$ to an abelian variety ${\mathcal{A}}$, all defined over a number field $k$. Suppose that $X$ is a counterexample to the Hasse principle. We give sufficient conditions for the failure of the Hasse principle on $X$ to be accounted for by the Brauer–Manin obstruction. These sufficiency conditions are slightly stronger than assuming that ${\mathcal{A}}(k)$ and ${\cyrX}({\mathcal{A}}/k)$ are finite.
LA - eng
UR - http://eudml.org/doc/249265
ER -
References
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