Some consequences of Arthur's work on the spectrum and topology of hyperbolic varieties

DOI10.1007/s00222-012-0415-2zbMath1309.22014OpenAlexW2009172023MaRDI QIDQ1955770

Nicolas Bergeron, Laurent Clozel

Publication date: 18 June 2013

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-012-0415-2

zbMATH Keywords

spectrumhyperbolic manifoldcongruence subgroupLaplacianautomorphic formLefschetz properties

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Cohomology of arithmetic groups (11F75)

Related Items (17)

The Shimura-Waldspurger correspondence for \(\mathrm{Mp}_{2n}\) ⋮ Effective estimates on integral quadratic forms: Masser's conjecture, generators of orthogonal groups, and bounds in reduction theory ⋮ On the spectrum and the topology of congruence hyperbolic varieties: the complex and quaternionic cases ⋮ Lefschetz properties for noncompact arithmetic ball quotients ⋮ Congruence RFRS towers ⋮ On the cohomology of trialitary hyperbolic varieties of dimension 7 ⋮ Almost complex structures on hyperbolic manifolds ⋮ Discrete components in restriction of unitary representations of rank one semisimple Lie groups ⋮ AUTOMORPHIC LEFSCHETZ PROPERTIES FOR NONCOMPACT ARITHMETIC MANIFOLDS ⋮ Stability and instability of lattices in semisimple groups ⋮ Limit theorems for rank-one Lie groups ⋮ The Hodge conjecture and arithmetic quotients of complex balls ⋮ The role of the Ramanujan conjecture in analytic number theory ⋮ Quantitative spectral gap for thin groups of hyperbolic isometries ⋮ Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds ⋮ Shrinking target problems for flows on homogeneous spaces ⋮ The Noether-Lefschetz conjecture and generalizations

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