Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms
By Frank Calegari, M. Emerton. 2007
60 citations recorded by the source corpus.
Let Goo be a semisimple real Lie group with unitary dual Goo- We produce new upper bounds for the multiplicities with which representations ^ e of cohomological type appear in certain spaces of cusp forms on Goo* The main new idea is to apply noncommutative Iwasawa theory to certain p-adic completions of the cohomology of locally symmetric spaces.
View Paper: https://www.semanticscholar.org/paper/7abb7eff9fff135cf345aa7e2b2cf7a0a4f658de
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Citations in the corpus
- Families of L -Functions and Their Symmetry (2014, result): “In the case at hand concerning these families for which B∞ is as above, there have been some conjectures and results concerning the sizes of these sets, see [91], [21], [74].”
- Torsion homology growth and cycle complexity of arithmetic manifolds (2014, background): “Heuristically, we expect (i) to be valid with very few exceptions, and (ii) to be always valid; see [16, 6] for evidence, and also [39] in a somewhat different direction.”
- The asymptotic growth of torsion homology for arithmetic groups (2010, background): “More generally, it is believed that the cohomology of Shimura varieties (all of which have δ = 0; for example, G= Spn(R), or G=O(2n,m), or G= U(n,m)) should have very little torsion – precise statements in a related vein are proposed in [17].”