Vol. 11, No. 1, 2017

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

Volume 11
Issue 4, 767–1007
Issue 3, 505–765
Issue 2, 253–503
Issue 1, 1–252

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
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Existence of compatible systems of lisse sheaves on arithmetic schemes

Koji Shimizu

Vol. 11 (2017), No. 1, 181–211
Abstract

Deligne conjectured that a single -adic lisse sheaf on a normal variety over a finite field can be embedded into a compatible system of -adic lisse sheaves with various . Drinfeld used Lafforgue’s result as an input and proved this conjecture when the variety is smooth. We consider an analogous existence problem for a regular flat scheme over and prove some cases using Lafforgue’s result and the work of Barnet-Lamb, Gee, Geraghty, and Taylor.

Keywords
arithmetic geometry, lisse sheaves, compatible system
Mathematical Subject Classification 2010
Primary: 11G35
Secondary: 11F80
Milestones
Received: 22 February 2016
Revised: 19 October 2016
Accepted: 17 November 2016
Published: 23 January 2017
Authors
Koji Shimizu
Department of Mathematics
Harvard University
Cambridge, MA 02138
United States