arXiv · 0907.0876
In this paper the third homology group of the linear group GL_2(R) with integral coefficients is investigated, where R is a commutative ring with many units.
B. Mirzaii. 2009-07-05. A note on third homology of GL_2. https://arxiv.org/abs/0907.0876
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The celebrated theorems of Shilov, Arens--Royden, and Forster give direct descriptions of the first three integral cohomology groups of the Gelfand spectrum of a commutative complex Banach algebra. In his 1974 ICM address, Taylor asked whether the higher cohomology groups admit descriptions in terms of the underlying ring. We give a solution to this question in even degrees: The \'etale (aka Lichtenbaum) Chow group in every codimension is canonically isomorphic to the corresponding even integral cohomology group of the Gelfand spectrum.
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