Eisenstein cohomology

General Introduction
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Online References
Here are some notes
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
arXiv:1103.0851 Eisenstein Cohomology and ratios of critical values of RankinSelberg Lfunctions from arXiv Front: math.AG by Guenter Harder, A. Raghuram This is an announcement of results on rankone Eisenstein cohomology of GL(N), with N > 1 an odd integer, and algebraicity theorems for ratios of successive critical values of certain RankinSelberg Lfunctions for GL(n) x GL(n') when n is even and n' is odd.
arXiv:1208.1747 Weight zero Eisenstein cohomology of Shimura varieties via Berkovich spaces from arXiv Front: math.NT by Michael Harris This brief article gives an alternative interpretation, based on a theorem of Berkovich, of the Eisenstein classes in the cohomology of Shimura varieties, used in forthcoming work of the author with K. W. Lan, R. Taylor, and J. Thorne.
[arXiv:1003.2326] Automorphic Forms, Cohomology and CAP Representations. The Case $GL2$ over a definite quaternion algebra from arXiv Front: math.NT by Harald Grobner In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL2$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree $1$. The latter ones turn out to be CAPrepresentations, though $G$ satisfies Strong Multiplicity One. A nonvanishing result on intertwining operators of induced representations will serve as a starting point for further investigations concerning rationality of critical $L$values.
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