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Cohomology of Congruence Subgroups of SU (2, 1)p and Hodge Cycles on Some Special Complex Hyperbolic Surfaces

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Regulators in Analysis, Geometry and Number Theory

Part of the book series: Progress in Mathematics ((PM,volume 171))

Abstract

Let G be a semisimple algebraic group over a number field F and set G = ∏ vS Gv, where S is the set of archimedean places of F. As is well-known, the cohomology of a cocompact lattice Γ ⊂ G is expressed in terms of the decomposition

$${L^2}\left( {\Gamma \backslash {G_\infty }} \right) \simeq \hat \oplus m(\pi ,\Gamma )\pi $$

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Blasius, D., Rogawski, J. (2000). Cohomology of Congruence Subgroups of SU (2, 1)p and Hodge Cycles on Some Special Complex Hyperbolic Surfaces. In: Reznikov, A., Schappacher, N. (eds) Regulators in Analysis, Geometry and Number Theory. Progress in Mathematics, vol 171. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1314-7_1

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  • DOI: https://doi.org/10.1007/978-1-4612-1314-7_1

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7089-8

  • Online ISBN: 978-1-4612-1314-7

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