Lei, Antonio, Loeffler, David and Zerbes, Sarah Livia (2017) On the asymptotic growth of Bloch-Kato--Shafarevich-Tate groups of modular forms over cyclotomic extensions. Canadian Journal of Mathematics, 69 . pp. 826-850. doi:10.4153/CJM-2016-034-x ISSN 0008-414X.

PDF WRAP_leiJ1713-AD.pdf - Accepted Version - Requires a PDF viewer. Download (803Kb)

Request Changes to record.

Abstract

We study the asymptotic behaviour of the Bloch--Kato--Shafarevich--Tate group of a modular form over the cyclotomic \mathbb{Z}_p-extension of \mathbb{Q} under the assumption that f is non-ordinary at p. In particular, we give upper bounds of these groups in terms of Iwasawa invariants of Selmer groups defined using p-adic Hodge Theory. These bounds have the same form as the formulae of Kobayashi, Kurihara and Sprung for supersingular elliptic curves.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Cyclotomic fields, Forms, Modular
Journal or Publication Title:	Canadian Journal of Mathematics
Publisher:	University of Toronto Press
ISSN:	0008-414X
Official Date:	August 2017
Dates:	Date Event August 2017 Published 6 December 2016 Available 29 September 2016 Accepted
Volume:	69
Page Range:	pp. 826-850
DOI:	10.4153/CJM-2016-034-x
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	4 October 2016
Date of first compliant Open Access:	4 October 2016
Funder:	Natural Sciences and Engineering Research Council of Canada (NSERC), Royal Society (Great Britain). University Research Fellowship, Leverhulme Trust (LT). Research Research Fellowship
Grant number:	Discovery Grants Program 05710 (NSERC)

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads