Homologie du groupe linéaire et K-théorie de Milnor des anneaux. (Homology of the linear group and Milnor's K-theory of rings)
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Publication:1118694
DOI10.1016/0021-8693(89)90033-1zbMath0669.20037OpenAlexW2037938151MaRDI QIDQ1118694
Publication date: 1989
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-8693(89)90033-1
Cohomology theory for linear algebraic groups (20G10) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Linear algebraic groups over adèles and other rings and schemes (20G35)
Related Items (21)
Some aspects of homotopic algebra and non-abelian (co)homology theories ⋮ Linear groups over general rings. I: Generalities. ⋮ Faithfully quadratic rings ⋮ Third homology of general linear groups over rings with many units ⋮ Stiefel-Whitney invariants for bilinear forms ⋮ Surjectivity of the total Clifford invariant and Brauer dimension ⋮ Homology of \(\mathrm{GL}_n\): injectivity conjecture for \(\mathrm{GL}_{4}\) ⋮ Third homology of general linear groups ⋮ A Bloch-Wigner exact sequence over local rings ⋮ Quadratic form theory over preordered von Neumann-regular rings ⋮ Deformations of Bloch groups and Aomoto dilogarithms in characteristic \(p\) ⋮ Two comparison theorems in étale cohomology; applications ⋮ Bloch-Wigner theorem over rings with many units. ⋮ Homology stability for orthogonal groups over algebraically closed fields ⋮ Motivic spheres and the image of the Suslin-Hurewicz map ⋮ A Note on Third Homology of GL2 ⋮ Homology of \(GL_n\) over infinite fields outside the stability range ⋮ Homology of tangent groups considered as discrete groups and scissors congruence ⋮ The indecomposable \(K_3\) of rings and homology of \(\text{SL}_2\) ⋮ Cohomology of crossed Lie algebras and additive Milnor's \(K\)- theory ⋮ A Bloch-Wigner theorem over rings with many units. II.
Cites Work
- Homology stability for linear groups
- Bass's first stable range condition
- Cyclic homology and the Lie algebra homology of matrices
- \(K_ 2\) of non-commutative local rings
- Homology of classical Lie groups made discrete. I: Stability theorems and Schur multipliers
- Comparaison des homologies du groupe linéaire et de son algèbre de Lie. (Comparison of homologies of a linear group and its Lie algebra)
- Cohomologie et homologie non abéliennes des groupes. (Nonabelian cohomology and homology of groups)
- Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
- Stable rank of rings and dimensionality of topological spaces
- Fundamental groups, algebraic K-theory, and a problem of Abhyankar
- \(K\)-theory and stable algebra
- $K$-théorie algébrique et représentations de groupes
- The $K_2$ of rings with many units
- Introduction to Algebraic K-Theory. (AM-72)
- ON THE STABILIZATION OF THE GENERAL LINEAR GROUP OVER A RING
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