Geodesic
Mixed Hodge complexes and $L^2$-cohomology for local systems on ball quotients
Documenta mathematica, Tome 17 (2012), pp. 517-543
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We study the L2-cohomology of certain local systems on non-compact arithmetic ball quotients X=Γ∖Bn​. In the case of a ball quotient surface X we show that vanishing theorems for L2-cohomology are intimately related to vanishing theorems of the type
DOI : 10.4171/dm/374
Classification : 14F17, 14G35, 32M15, 32Q30
Mots-clés : Shimura variety, abelian variety, uniformization, Higgs bundle, ball quotient, mixed Hodge theory, monodromy representation 
@article{10_4171_dm_374,
     author = {Xuanming Ye and Stefan M\"uller-Stach and Kang Zuo},
     title = {Mixed {Hodge} complexes and $L^2$-cohomology for local systems on ball quotients},
     journal = {Documenta mathematica},
     pages = {517--543},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/374},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/374/}
}
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Xuanming Ye; Stefan Müller-Stach; Kang Zuo. Mixed Hodge complexes and $L^2$-cohomology for local systems on ball quotients. Documenta mathematica, Tome 17 (2012), pp. 517-543. doi: 10.4171/dm/374

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