On the K-theory of elliptic curves, by 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 field of X. We show that the image of H*(GL2(A),Z) in H*(GL2(F),Z) coincides with the image of H*(GL2(k),Z). As a consequence, we obtain numerous results about the K-theory of A and X. For example, if k is a number field, we show that r2 K2(A)Q = 0, where rm denotes the mth level of the rank filtration.

Note: the dvi file has missing figures; they are included in the PS file.

Kevin P. Knudson <knudson@math.nwu.edu>