Rational points of the group of components¶of a Néron model

Siegfried Bosch; Qing Liu

DOI:10.1007/s002290050140
Corpus ID: 14838089

Rational points of the group of components¶of a Néron model

@article{Bosch1998RationalPO,
  title={Rational points of the group of components¶of a N{\'e}ron model},
  author={Siegfried Bosch and Qing Liu},
  journal={manuscripta mathematica},
  year={1998},
  volume={98},
  pages={275-293}
}

Siegfried Bosch, Qing Liu
Published 14 April 1998
Mathematics
manuscripta mathematica

Abstract:The structure of component groups of Néron models has been investigated on several occasions. Here we admit non-separably closed residue fields and are interested in the subgroup of rational points or, in other terms, in the subgroup of geometrically connected components of a Néron model. We consider Néron models of abelian varieties and of algebraic tori and give detailed computations in the case of Jacobians of curves.

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References

SHOWING 1-10 OF 17 REFERENCES

SORT BY

The scheme of connected components of the Néron model of an algebraic torus.

X. Xarles
Mathematics
1993

where ^"° denotes the connected component of &l The aim of this paper is to describe the sheaf of connected components of «^ in terms of the character group 9 Gm). Since &~/&~° is a skyscraper sheaf,…

Modular curves and the eisenstein ideal

B. Mazur
Mathematics
1977

Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer

W. J. Gordon
Mathematics
1979

Cohomology of groups

L. Evens
Engineering
Oxford mathematical monographs
1991

A rink-type roller skate is provided with a plastic sole plate. To mount a toe stop on the skate, a novel bushing is embedded in the sole plate. The bushing has relatively small diameter ends and a…