Cohomology of arithmetic groups

General Introduction
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Search results
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Online References
A possible reference is the Burgos book on the Borel regulator.
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Paper References
Book by Armand Borel
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
arXiv:1008.3664 On the geometry of global function fields, the RiemannRoch theorem, and finiteness properties of Sarithmetic groups from arXiv Front: math.AG by Ralf Gramlich Harder's reduction theory provides filtrations of euclidean buildings that allow one to deduce cohomological and homological properties of Sarithmetic groups over global function fields. In this survey I will sketch the main points of Harder's reduction theory starting from Weil's geometry of numbers and the RiemannRoch theorem, describe a filtration that is particularly useful for deriving finiteness properties of Sarithmetic groups, and state the rank conjecture and its partial verifications that do not restrict the cardinality of the underlying field of constants. As a motivation for further research I also state a much more general conjecture on isoperimetric properties of Sarithmetic groups over global fields (number fields or function fields).
arXiv:1001.0789 Perfect forms and the cohomology of modular groups from arXiv Front: math.NT by Philippe ElbazVincent, Herbert Gangl, Christophe SoulĂ© For N=5, 6 and 7, using the classification of perfect quadratic forms, we compute the homology of the Voronoi cell complexes attached to the modular groups SLN(\Z) and GLN(\Z). From this we deduce the rational cohomology of those groups.
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Other Information
http://mathoverflow.net/questions/3701/stablehomologyofarithmeticgroups
Apparently this cohomology can also be interpreted as cohomology of some moduli spaces, see for example answers to this question: http://mathoverflow.net/questions/805/cohomologyofmodulispaces
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