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- Publisher
- de Gruyter
- Copyright
- © 2019 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/forum-2019-0029
- Publisher site
- See Article on Publisher Site
Abstract
AbstractThe cohomology of an arithmetic congruence subgroupof a connected reductive algebraic group definedover a number field is captured in theautomorphic cohomology of that group.The residual Eisenstein cohomology is by definition the part of theautomorphic cohomology represented by square-integrableresidues of Eisenstein series. The existence ofresidual Eisenstein cohomology classes depends ona subtle combination of geometric conditions (comingfrom cohomological reasons) and arithmetic conditionsin terms of analytic properties of automorphicL-functions (coming from the study of polesof Eisenstein series). Hence,there are almost nounconditional results in the literature regarding the very existenceof non-trivial residual Eisenstein cohomology classes. In thispaper, we show the existence of certain non-trivial residualcohomology classes in the case of the split symplectic,and odd and even special orthogonal groups of ranktwo, as well as the exceptional group of type G2{\mathrm{G}_{2}},defined over a totally real number field.The construction of cuspidal automorphic representations of GL2{\mathrm{GL}_{2}}withprescribed local and global properties is decisive in this context.
Journal
Forum Mathematicum – de Gruyter
Published: Sep 1, 2019