3 citations · 11 across the 18 of their papers we have counts for
5 papers · 1 filter
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…
Relative completions of linear groups over Z[t] and Z[t,t^{-1}]
Kevin P. Knudson
We compute the completion of the groups SL_n(Z[t]) and SL_n(Z[t,t^{-1}]) relative to the obvious homomorphisms to SL_n(Q); this is a generalization of the classical Malcev completi…
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.…
Low dimensional homology of linear groups over Hensel local rings
Kevin P. Knudson
We prove that if R is a Hensel local ring with infinite residue field k, the natural map H_i(GL(n,R),Z/p) ---> H_i(GL(n,k),Z/p) is an isomorphism for i <=3, p distinct from char(k)…