On the Eisenstein cohomology of odd orthogonal groups

Gerald Gotsbacher, Harald Grobner

Type: Article

Publication Date: 2011-05-05

Citations: 7

DOI: https://doi.org/10.1515/form.2011.118

Abstract

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes for maximal parabolic Q-subgroups in case of generic cohomological cuspidal automorphic representations of their Levi subgroups. That is, such identifying necessary conditions on these latter representations as well as on the complex parameters in order for the associated Eisenstein series to possibly yield non-trivial classes in the automorphic cohomology.

Locations

arXiv (Cornell University) - View - PDF
MPG.PuRe (Max Planck Society) - View - PDF
DataCite API - View
Forum Mathematicum - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Eisenstein cohomology for congruence subgroups of SO(n, 2)	2009	Gerald Gotsbacher
+	Some consequences of Arthur's conjectures for special orthogonal even groups	2009	Octavio Paniagua-Taboada
+ PDF Chat	GALOIS REPRESENTATIONS FOR EVEN GENERAL SPECIAL ORTHOGONAL GROUPS	2023	Arno Kret Sug Woo Shin
+	Galois representations for even general special orthogonal groups	2020	Arno Kret Sug Woo Shin
+	On the Eisenstein cohomology of arithmetic groups	2004	Jianshu Li Joachim Schwermer
+ PDF Chat	On arithmetic subgroups of a Q-rank 2 form of SU(2,2) and their automorphic cohomology	2005	Takahiro Hayata Joachim Schwermer
+	Some conjectures on endoscopic representations in odd orthogonal groups	2012	David Ginzburg Dihua Jiang
+	Eisenstein series and automorphic forms orthogonal to cusp forms	1997	Armand Borel
+ PDF Chat	Some consequences of Arthur's conjectures for special orthogonal even groups	2011	Octavio Paniagua-Taboada
+ PDF Chat	On the images of the Galois representations attached to certain RAESDC automorphic representations of $\mathrm{GL}_n (\mathbb{A}_\mathbb{Q})$	2019	Adrián Zenteno
+ PDF Chat	Some conjectures on endoscopic representations in odd orthogonal groups	2012	David Ginzburg Dihua Jiang
+ PDF Chat	A construction of residues of Eisenstein series and related square-integrable classes in the cohomology of arithmetic groups of low <i>k</i>-rank	2019	Neven Grbac Joachim Schwermer
+	A weak form of beyond endoscopic decomposition for the stable trace formula of odd orthogonal groups	2016	Chung Pang Mok
+	A weak form of beyond endoscopic decomposition for the stable trace formula of odd orthogonal groups	2016	Chung Pang Mok
+	A family of square integrable representations of classical p-adic groups in the case of general half-integral reducibilities	2002	Marko Tadić
+ PDF Chat	On Eisenstein series and the cohomology of arithmetic groups	2010	Neven Grbac Joachim Schwermer
+ PDF Chat	Regular and residual Eisenstein series and the automorphic cohomology of Sp(2,2)	2009	Harald Grobner
+	Eisenstein cohomology for congruence subgroups of SO(n,2)	2008	Gerald Gotsbacher
+	On quadratic distinction of automorphic sheaves	2011	Yifeng Liu
+	Theta lifts to certain cohomological representations of indefinite orthogonal groups	2023	Takuya Miyazaki Saito Yohei

Works That Cite This (7)

Action	Title	Year	Authors
+ PDF Chat	Residues of Eisenstein series and the automorphic cohomology of reductive groups	2013	Harald Grobner
+	Arithmeticity for periods of automorphic forms	2012	Wee Teck Gan A. Raghuram
+	Image des opérateurs dʼentrelacements normalisés et pôles des séries dʼEisenstein	2011	Colette Mœglin
+ PDF Chat	Ghost classes in $${\mathbb {Q}}$$-rank two orthogonal Shimura varieties	2020	Jitendra Bajpai Matías Victor Moya Giusti
+	Eisenstein Cohomology and Automorphic L-Functions	2018	Neven Grbac
+ PDF Chat	On the arithmetic of Shalika models and the critical values of L -functions for GL 2 n	2014	Harald Grobner A. Raghuram Wee Teck Gan
+	On the arithmetic of Shalika models and the critical values of $L$-functions for ${\rm GL}(2n)$	2011	Harald Grobner A. Raghuram

Works Cited by This (23)

Action	Title	Year	Authors
+	Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups	2000	A. Borel Nolan R. Wallach
+	None	2001	Henry Kim
+	Langlands–Shahidi method and poles of automorphic L-functions III: Exceptional groups	2007	Henry H. Kim
+	The Multiplicity One Theorem for GL n	1974	J. A. Shalika
+ PDF Chat	Harmonic analysis in weighted L2-spaces	1998	Jens Frankē
+	Structure Arising from Induction and Jacquet Modules of Representations of Classical p-Adic Groups	1995	Marko Tadić
+	A decomposition of spaces of automorphic forms, and the Eisenstein cohomology of arithmetic groups	1998	Jens Frankē Joachim Schwermer
+ PDF Chat	Functoriality for the classical groups	2004	James Cogdell H. H. Kim Ilya Piatetski-Shapiro Freydoon Shahidi
+	THE AUTOMORPHIC COHOMOLOGY AND THE RESIDUAL SPECTRUM OF HERMITIAN GROUPS OF RANK ONE	2010	Harald Grobner
+	On Certain L-Functions	1981	Freydoon Shahidi