Homogeneous spaces, algebraic $K$-theory and cohomological dimension of fields

Cohomological Dimension Theory of Compact Metric Spaces

0. Introduction 1 1. General properties of the cohomological dimension 2 2. Bockstein theory 6 3. Cohomological dimension of Cartesian product 10 4. Dimension type algebra 15 5. Realization theorem 19 6. Test spaces 24 7. Infinite-dimensional compacta of finite cohomological dimension 28 8. Resolution theorems 33 9. Resolutions preserving cohomological dimensions 41 10. Imbedding and approximat...

Algebraic K - Theory and Configuration Spaces

Its importance lies in the fact that the right hand side of the above equivalence (which wewill briefly refer to as a configuration space model) is a much smaller space than the function space on the left, and thus is much easier to deal with. The second author noted that in the configuration space model, one can replace the X" by spaces like BGln(R). For there is an obvious ~n action on BGln(R...

Algebraic Homogeneous Spaces over Fields of Characteristic Two

Algebraic K-theory of Finite Fields

Derived Representation Theory and the Algebraic K-theory of Fields

Quillen’s higher algebraic K-theory for fields F has been the object of intense study since their introduction in 1972 [26]. The main direction of research has been the construction of “descent spectral sequences” whose E2-term involved the cohomology of the absolute Galois groupGF with coefficients in the algebraic K–theory of an algebraically closed. The form of such a spectral sequence was c...