The Library
Density of classical points in eigenvarieties
Tools
Loeffler, David (2011) Density of classical points in eigenvarieties. Mathematical Research Letters, Vol.18 (No.5). pp. 983-990. ISSN 1945-001X.
|
PDF
WRAP_Loeffler_eigenvarieties_.asp.pdf - Accepted Version - Requires a PDF viewer. Download (344Kb) |
Official URL: http://mrlonline.org/jourcgi/jrnl_toolbar_nav/mrl_...
Abstract
In this short note, we study the geometry of the eigenvariety parametrizing p-adic automorphic forms for GL(1) over a number field, as constructed by Buzzard. We show that if K is not totally real and contains no CM subfield, points in this space arising from classical automorphic forms (i.e. algebraic Grossencharacters of K) are not Zariski-dense in the eigenvariety (as a rigid space); but the eigenvariety posesses a natural formal scheme model, and the set of classical points is Zariski-dense in the formal scheme.
We also sketch the theory for GL(2) over an imaginary quadratic field, following Calegari and Mazur, emphasizing the strong formal similarity with the case of GL(1) over a general number field.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Automorphic forms | ||||
Journal or Publication Title: | Mathematical Research Letters | ||||
Publisher: | Mathematical Publishing | ||||
ISSN: | 1945-001X | ||||
Official Date: | September 2011 | ||||
Dates: |
|
||||
Volume: | Vol.18 | ||||
Number: | No.5 | ||||
Page Range: | pp. 983-990 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 18 December 2015 | ||||
Date of first compliant Open Access: | 18 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP/F04304X/2 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year