Geometric cycles, arithmetic groups and their cohomology
نویسندگان
چکیده
منابع مشابه
Weighted cohomology of arithmetic groups
Let G be a semisimple algebraic group defined over the rational numbers, K a maximal compact subgroup of G = G(R), and Γ ⊂ G(Q) a neat arithmetic subgroup. LetX = Γ\G/K be the locally symmetric space associated to Γ, and E the local system on X constructed out of a finite-dimensional, irreducible, algebraic representation E of G. Fix a maximally Q-split torus S in G; S is assumed to be nontrivi...
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These lectures will be mainly concerned with the real or complex cohomology of an arithmetic subgroup Γ of a semisimple Q-group G. It can be identified to the cohomology of the quotient Γ \ X by Γ of the space X of maximal compact subgroups of G, which has allowed one to study the cohomology of Γ by a variety of methods: geometric constructions, de Rham and Lie algebra cohomology, harmonic and ...
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(1) Firstly, I gave a brief introduction to the cohomology of arithmetic groups, in particular the fact that the “tempered” (informally: “near the middle dimension”’) part of the cohomology looks like the cohomology of a torus. This corresponds to §2, §3, §4 of these notes. For the reader totally unfamiliar with the cohomology of arithmetic groups, §3 might be the best thing to focus on. (2) Ne...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2010
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-10-01292-9