Congruence cohomology conjecture for groups with discrete series

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Let GG be a semisimple group with discrete series. Let π∈G^\pi\in\widehat G be a cohomological representation, and consider the question of whether there is a lattice Γ\Gamma in GG such that π\pi occurs discretely in L2(Γ\G)L^2(\Gamma\backslash G). Congruence cohomology conjecture. The answer to this question is always positive for GG. The assertion is presented as a consequence of the automorphic functoriality and isolation conjectures, and is not established unconditionally in the source.

References

Primary source

N. Bergeron, “Représentations cohomologiques isolées, applications cohomologiques”, arXiv:math/0511689 (2005).

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