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作者：Vatsal, V
作者单位：University of British Columbia
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作者：Fang, FQ; Rong, XC
作者单位：Nankai University; Beijing Normal University; Rutgers University System; Rutgers University New Brunswick
摘要：Let M-i -->(dGH) X denote a sequence of n-manifolds converging to a compact metric space, X, in the Gromov-Hausdorff topology such that the sectional curvature is bounded in absolute value and dim(X) < n. We prove the following stability result: If the fundamental groups of M-i are torsion groups of uniformly bounded exponents and the second twisted Betti numbers of M-i vanish, then there is a manifold, M, and a sequence of diffeomorphisms from M to a subsequence of {M-i} such that the distanc...
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作者：Lück, W
作者单位：University of Munster
摘要：We prove a version of the L-2-index Theorem of Atiyah, which uses the universal center-valued trace instead of the standard trace. We construct for G-equivariant K-homology an equivariant Chem character, which is an isomorphism and lives over the ring Z subset of Lambda(G) subset of Q obtained from the integers by inverting the orders of all finite subgroups of G. We use these two results to show that the Baum-Connes Conjecture implies the modified Trace Conjecture, which says that the image o...
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作者：Wilking, B
作者单位：University of Pennsylvania
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作者：Puschnigg, M
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
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作者：Lafforgue, L
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Universite Paris Saclay
摘要：One proves Langlands' correspondence for GL, over function fields. This is a generalization of Drinfeld's proof in the case of rank 2 : Langlands' correspondence is realized in l-adic cohomology spaces of the modular varieties classifying rank r Drinfeld shtukas.
