Vol. 16, No. 2, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
This article is available for purchase or by subscription. See below.
Rank 2 local systems, Barsotti–Tate groups, and Shimura curves

Raju Krishnamoorthy

Vol. 16 (2022), No. 2, 231–259
Abstract

We construct a descent-of-scalars criterion for K-linear abelian categories. Using advances in the Langlands correspondence due to Abe, we build a correspondence between certain rank 2 local systems and certain Barsotti–Tate groups on complete curves over a finite field. We conjecture that such Barsotti–Tate groups “come from” a family of fake elliptic curves. As an application of these ideas, we provide a criterion for being a Shimura curve over 𝔽q. Along the way we formulate a conjecture on the field-of-coefficients of certain compatible systems.

PDF Access Denied

We have not been able to recognize your IP address 35.170.81.33 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Shimura curves, Barsotti–Tate groups, local systems
Mathematical Subject Classification 2010
Primary: 14G15
Secondary: 14G35, 14H25
Milestones
Received: 20 March 2019
Revised: 2 June 2021
Accepted: 7 July 2021
Published: 27 April 2022
Authors
Raju Krishnamoorthy
Bergische Universität Wuppertal
Germany