Congruence cohomology conjecture for groups with discrete series
Let be a semisimple group with discrete series. Let be a cohomological representation, and consider the question of whether there is a lattice in such that occurs discretely in . Congruence cohomology conjecture. The answer to this question is always positive for . 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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