On the galois structure of selmer groups

David Burns; Daniel Mac Ias Castillo; Christian Wuthrich

doi:10.1093/imrn/rnv045

On the galois structure of selmer groups

David Burns, Daniel Mac Ias Castillo^*, Christian Wuthrich

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F, we investigate the explicit Galois structure of the p-primary Selmer group of A over F. We also use the results so obtained to derive new bounds on the growth of the Selmer rank of A over extensions of k.

Original language	English
Pages (from-to)	11909-11933
Number of pages	25
Journal	International Mathematics Research Notices
Volume	2015
Issue number	22
Early online date	25 Feb 2015
DOIs	https://doi.org/10.1093/imrn/rnv045
Publication status	E-pub ahead of print - 25 Feb 2015

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10.1093/imrn/rnv045

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AB - Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F, we investigate the explicit Galois structure of the p-primary Selmer group of A over F. We also use the results so obtained to derive new bounds on the growth of the Selmer rank of A over extensions of k.

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On the galois structure of selmer groups

Abstract

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