A bound for the average rank of a family of abelian varieties

Rania Wazir

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 1, page 241-252
  • ISSN: 0392-4041

Abstract

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In this note, we consider a one-parameter family of Abelian varieties A / Q T , and find an upper bound for the average rank in terms of the generic rank. This bound is based on Michel's estimates for the average rank in a one-parameter family of Abelian varieties, and extends previous work of Silverman for elliptic surfaces.

How to cite

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Wazir, Rania. "A bound for the average rank of a family of abelian varieties." Bollettino dell'Unione Matematica Italiana 7-B.1 (2004): 241-252. <http://eudml.org/doc/195136>.

@article{Wazir2004,
abstract = {In this note, we consider a one-parameter family of Abelian varieties $A/ \mathbb\{Q\}(T)$, and find an upper bound for the average rank in terms of the generic rank. This bound is based on Michel's estimates for the average rank in a one-parameter family of Abelian varieties, and extends previous work of Silverman for elliptic surfaces.},
author = {Wazir, Rania},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {241-252},
publisher = {Unione Matematica Italiana},
title = {A bound for the average rank of a family of abelian varieties},
url = {http://eudml.org/doc/195136},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Wazir, Rania
TI - A bound for the average rank of a family of abelian varieties
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/2//
PB - Unione Matematica Italiana
VL - 7-B
IS - 1
SP - 241
EP - 252
AB - In this note, we consider a one-parameter family of Abelian varieties $A/ \mathbb{Q}(T)$, and find an upper bound for the average rank in terms of the generic rank. This bound is based on Michel's estimates for the average rank in a one-parameter family of Abelian varieties, and extends previous work of Silverman for elliptic surfaces.
LA - eng
UR - http://eudml.org/doc/195136
ER -

References

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