Holmstrom Cohomology of arithmetic groups

Cohomology of arithmetic groups

There are lots of thing on the K-theory archive, not linked to from here.

Should check everything by Borel.

Some random references:

MR0578905 (58 #28281) 22E40 (12A70) Borel, Armand Cohomology of arithmetic groups. Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974), Vol. 1, pp. 435?442. Canad. Math. Congress, Montreal, Que., 1975. The author gives a survey of results, mostly due to himself and J.-P. Serre, on the Eilenberg- Mac Lane cohomology groups of an arithmetic or S-arithmetic subgroup of a reductive affine algebraic group defined over an algebraic number field with coefficients in a ∞-module E (e.g., R or C). This is related to the regulator of the ground field and to the values of the ∞-function of the field at odd negative integers. A more recent and more extended survey has appeared elsewhere [#28282 below]. {For the entire collection see MR0411878 (54 #7).}

category: [Private] Notes


Cohomology of arithmetic groups

MathSciNet

Google Scholar

Google

arXiv: Experimental full text search

arXiv: Abstract search

category: Search results


Cohomology of arithmetic groups

RT (Groups and representation theory)

category: World [private]


Cohomology of arithmetic groups

Book by Armand Borel

category: Paper References


Cohomology of arithmetic groups

http://mathoverflow.net/questions/3701/stable-homology-of-arithmetic-groups

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/cohomology-of-moduli-spaces


Cohomology of arithmetic groups

arXiv:1008.3664 On the geometry of global function fields, the Riemann-Roch theorem, and finiteness properties of S-arithmetic 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 S-arithmetic 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 Riemann-Roch theorem, describe a filtration that is particularly useful for deriving finiteness properties of S-arithmetic 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 S-arithmetic 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 Elbaz-Vincent, Herbert Gangl, Christophe Soulé 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 SL_N(\Z) and GL_N(\Z). From this we deduce the rational cohomology of those groups.


Cohomology of arithmetic groups

A possible reference is the Burgos book on the Borel regulator.

nLab page on Cohomology of arithmetic groups

Created on June 10, 2014 at 21:14:54 by Andreas Holmström