Asset Details
Do you wish to reserve the book?
Parity-induced Selmer Growth For Symplectic, Ordinary Families
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Parity-induced Selmer Growth For Symplectic, Ordinary Families
Do you wish to request the book?
Parity-induced Selmer Growth For Symplectic, Ordinary Families
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Paper
Parity-induced Selmer Growth For Symplectic, Ordinary Families
2008
Overview
Let \\(p\\) be an odd prime, and let \\(K/K_0\\) be a quadratic extension of number fields. Denote by \\(K_\\pm\\) the maximal \\(\\mathbb{Z}_p\\)-power extensions of \\(K\\) that are Galois over \\(K_0\\), with \\(K_+\\) abelian over \\(K_0\\) and \\(K_-\\) dihedral over \\(K_0\\). In this paper we show that for a Galois representation over \\(K_0\\) satisfying certain hypotheses, if it has odd Selmer rank over \\(K\\) then for one of \\(K_\\pm\\) its Selmer rank over \\(L\\) is bounded below by \\([L:K]\\) for \\(L\\) ranging over the finite subextensions of \\(K\\) in \\(K_\\pm\\). Our method or proof generalizes a method of Mazur--Rubin, building upon results of Nekovář, and applies to abelian varieties of arbitrary dimension, (self-dual twists of) modular forms of even weight, and (twisted) Hida families.
Publisher
Cornell University Library, arXiv.org
Subject
