Growth of Sha in towers for isogenous curves

Tim Dokchitser; Vladimir Dokchitser

doi:10.1112/S0010437X15007423

Growth of Sha in towers for isogenous curves

Tim Dokchitser, Vladimir Dokchitser

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Abstract

We study the growth of the Tate-Shafarevich and p-infinity Selmer groups for isogenous abelian varieties in towers of number fields, with an emphasis on elliptic curves. The growth types are usually exponential, as in the setting of `positive mu-invariant' in Iwasawa theory of elliptic curves. The towers we consider are p-adic and l-adic Lie extensions for l p, in particular cyclotomic and other Z_l-extensions.

Original language	English
Journal	Compositio Mathematica
Early online date	30 Jun 2015
DOIs	https://doi.org/10.1112/S0010437X15007423
Publication status	E-pub ahead of print - 30 Jun 2015

Bibliographical note

28 pages

Keywords

math.NT
11G07 (Primary), 11G05, 11G10, 11G40, 11R23 (Secondary)

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10.1112/S0010437X15007423

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Professor Tim Dokchitser
- Tim.Dokchitserbristol.acuk
- School of Mathematics - Heilbronn Chair in Algebraic/Arithmetic Geometry
- Pure Mathematics
- Number theory and combinatorics
Person: Academic , Member

Cite this

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AB - We study the growth of the Tate-Shafarevich and p-infinity Selmer groups for isogenous abelian varieties in towers of number fields, with an emphasis on elliptic curves. The growth types are usually exponential, as in the setting of `positive mu-invariant' in Iwasawa theory of elliptic curves. The towers we consider are p-adic and l-adic Lie extensions for l p, in particular cyclotomic and other Z_l-extensions.

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M3 - Article (Academic Journal)

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ER -

Growth of Sha in towers for isogenous curves

Abstract

Bibliographical note

Keywords

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Professor Tim Dokchitser

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