Vol. 10, No. 3, 2016

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

Volume 19, 1 issue

Volume 18, 12 issues

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
Regularized theta lifts and (1,1)-currents on GSpin Shimura varieties

Luis E. Garcia

Vol. 10 (2016), No. 3, 597–644
Abstract

We introduce a regularized theta lift for reductive dual pairs (Sp4,O(V )), for V a quadratic vector space over a totally real number field. The lift takes values in the space of (1,1)-currents on the Shimura variety attached to GSpin(V ); we show its values are cohomologous to currents given by integration on special divisors against automorphic Green functions. A later paper will show how to evaluate the new lift on differential forms obtained as usual (nonregularized) theta lifts.

Keywords
Shimura varieties, theta series, Weil representation
Mathematical Subject Classification 2010
Primary: 11F27
Secondary: 11F67, 11G18, 14G35
Milestones
Received: 8 May 2015
Revised: 9 December 2015
Accepted: 4 February 2016
Published: 12 June 2016
Authors
Luis E. Garcia
Department of Mathematics, South Kensington Campus
Imperial College London
London
SW7 2AZ
United Kingdom
Department of Mathematics
University of Toronto
40 St. George Street, BA 6290
Toronto, ON M5S 2E4
Canada