Component groups of abelian varieties and Grothendieck's duality conjecture

Siegfried Bosch

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 5, page 1257-1287
  • ISSN: 0373-0956

Abstract

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We investigate Grothendieck’s pairing on component groups of abelian varieties from the viewpoint of rigid uniformization theory. Under the assumption that the pairing is perfect, we show that the filtrations, as introduced by Lorenzini and in a more general way by Bosch and Xarles, are dual to each other. Furthermore, the methods yield some progress on the perfectness of the pairing itself, in particular, for abelian varieties with potentially multiplicative reduction.

How to cite

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Bosch, Siegfried. "Component groups of abelian varieties and Grothendieck's duality conjecture." Annales de l'institut Fourier 47.5 (1997): 1257-1287. <http://eudml.org/doc/75263>.

@article{Bosch1997,
abstract = {We investigate Grothendieck’s pairing on component groups of abelian varieties from the viewpoint of rigid uniformization theory. Under the assumption that the pairing is perfect, we show that the filtrations, as introduced by Lorenzini and in a more general way by Bosch and Xarles, are dual to each other. Furthermore, the methods yield some progress on the perfectness of the pairing itself, in particular, for abelian varieties with potentially multiplicative reduction.},
author = {Bosch, Siegfried},
journal = {Annales de l'institut Fourier},
keywords = {abelian varieties; Néron model; component group; Grothendieck's pairing; complete discrete valuation ring; rigid uniformization; dual variety},
language = {eng},
number = {5},
pages = {1257-1287},
publisher = {Association des Annales de l'Institut Fourier},
title = {Component groups of abelian varieties and Grothendieck's duality conjecture},
url = {http://eudml.org/doc/75263},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Bosch, Siegfried
TI - Component groups of abelian varieties and Grothendieck's duality conjecture
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 5
SP - 1257
EP - 1287
AB - We investigate Grothendieck’s pairing on component groups of abelian varieties from the viewpoint of rigid uniformization theory. Under the assumption that the pairing is perfect, we show that the filtrations, as introduced by Lorenzini and in a more general way by Bosch and Xarles, are dual to each other. Furthermore, the methods yield some progress on the perfectness of the pairing itself, in particular, for abelian varieties with potentially multiplicative reduction.
LA - eng
KW - abelian varieties; Néron model; component group; Grothendieck's pairing; complete discrete valuation ring; rigid uniformization; dual variety
UR - http://eudml.org/doc/75263
ER -

References

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