Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-54cdcc668b-zz2mb Total loading time: 0.341 Render date: 2021-03-08T22:35:22.731Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Compositio Mathematica Compositio Mathematica

Article contents

On the image of complex conjugation in certain Galois representations

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  23 May 2016

Ana Caraiani  and
Bao V. Le Hung
Ana Caraiani
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Rd., Princeton, NJ 08544, USA email caraiani@princeton.edu
Bao V. Le Hung
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA email lhvietbao@googlemail.com
Corresponding
E-mail address:
caraiani@princeton.edu
lhvietbao@googlemail.com
Get access
Rights & Permissions[Opens in a new window]

Abstract

We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for $\text{GL}_{n}$ over a totally real field $F$ .

Keywords

Galois representations torsion classes locally symmetric spaces local–global compatibility

MSC classification

Primary: 11F80: Galois representations
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 7 , July 2016 , pp. 1476 - 1488
Copyright
© The Authors 2016 

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

References

Arthur, J., The endoscopic classification of representations: orthogonal and symplectic groups, American Mathematical Society Colloquium Publications, vol. 61 (American Mathematical Society, Providence, RI, 2013).CrossRefGoogle Scholar
Ash, A. and Stevens, G., Cohomology of arithmetic groups and congruences between systems of Hecke eigenvalues , J. reine angew. Math. 365 (1986), 192–220.Google Scholar
Borel, A. and Serre, J.-P., Corners and arithmetic groups , Comment. Math. Helv. 48 (1973), 436–491; avec un appendice: Arrondissement des variétés à coins, par A. Douady et L. Hérault.CrossRefGoogle Scholar
Goresky, M., Harder, G. and MacPherson, R., Weighted cohomology , Invent. Math. 116 (1994), 139–213.CrossRefGoogle Scholar
Harris, M., Lan, K.-W., Taylor, R. and Thorne, J., On the rigid cohomology of certain Shimura varieties, Preprint (2014), arXiv:1411.6717 [math.NT].Google Scholar
Harris, M. and Taylor, R., The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151 (Princeton University Press, Princeton, NJ, 2001); with an appendix by V. G. Berkovich; MR 1876802 (2002m:11050).Google Scholar
Scholze, P., On torsion in the cohomology of locally symmetric varieties , Ann. of Math. (2) 185 (2015), 945–1066.CrossRefGoogle Scholar
Taibi, O., Eigenvarieties for classical groups and complex conjugations in Galois representations, Math. Res. Lett., to appear. Preprint (2012), arXiv:1203.0225 [math.NT].Google Scholar
Taylor, R., The image of complex conjugation in l-adic representations associated to automorphic forms , Algebra Number Theory 6 (2012), 405–435.CrossRefGoogle Scholar

Altmetric attention score

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 94 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 8th March 2021. This data will be updated every 24 hours.

3 Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

On the image of complex conjugation in certain Galois representations
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

On the image of complex conjugation in certain Galois representations
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

On the image of complex conjugation in certain Galois representations
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *