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

Research output: Contribution to journal › Article (Academic Journal) › peer-review

7 Citations (Scopus)

33 Downloads (Pure)

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)

Access to Document

10.1112/S0010437X15007423

Handle.net

Persistent link

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

@article{875f080d105a40b7a7f7aedaeffdf996,

title = "Growth of Sha in towers for isogenous curves",

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.",

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

author = "Tim Dokchitser and Vladimir Dokchitser",

note = "28 pages",

year = "2015",

month = jun,

day = "30",

doi = "10.1112/S0010437X15007423",

language = "English",

journal = "Compositio Mathematica",

issn = "0010-437X",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Growth of Sha in towers for isogenous curves

AU - Dokchitser, Tim

AU - Dokchitser, Vladimir

N1 - 28 pages

PY - 2015/6/30

Y1 - 2015/6/30

N2 - 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.

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.

KW - math.NT

KW - 11G07 (Primary), 11G05, 11G10, 11G40, 11R23 (Secondary)

U2 - 10.1112/S0010437X15007423

DO - 10.1112/S0010437X15007423

M3 - Article (Academic Journal)

SN - 0010-437X

JO - Compositio Mathematica

JF - Compositio Mathematica

ER -

Growth of Sha in towers for isogenous curves

Abstract

Bibliographical note

Keywords

Access to Document

Handle.net

Fingerprint

Profiles

Professor Tim Dokchitser

Cite this