3 citations · 11 across the 18 of their papers we have counts for
7 papers · 1 filter
Relative completions and of curves
Kevin P. Knudson
We compute the completion of the special linear group over the coordinate ring of a curve over a number field relative to its representation in $\slnk$, and relate this to the…
Homology of linear groups via cycles in
Kevin P. Knudson, Mark E. Walker
Let G be an algebraic group and let X be a smooth integral scheme over a field k. In this paper we construct homology-type groups by considering cycles in the simplicial…
Relative completions and the cohomology of linear groups over local rings
Kevin P. Knudson
We study the completion of a group relative to a Zariski dense representation in a reductive algebraic group over a field . The characteristic zero case was worked out previousl…
On the K-theory of elliptic curves
Kevin P. Knudson
Let A be the coordinate ring of an affine elliptic curve (over an infinite field k) of the form X-{p}, where X is projective and p is a closed point on X. Denote by F the function…
Amalgamated free products, unstable homotopy invariance, and the homology of SL_2(Z[t])
Kevin P. Knudson
We show that if R is an integral domain with many units, then the inclusion E_2(R) --> E_2(R[t]) induces an isomorphism in integral homology. This is a consequence of the existence…
Congruence subgroups and twisted cohomology of SL_n(F[t])
Kevin P. Knudson
Let F be a field of characteristic zero and let V be an irreducible representation of SL_n(F). In this paper, we compute the first cohomology of SL_n(F[t]) with coefficients in V.…