On the K-theory of elliptic curves

1998/09/29 by Kevin P. Knudson
Mathematics · #math.KT #math.AG #msc:19D55 #msc:20G10

paper · pdf

published as J. reine angew. Math. 507 (1999), 81-91 · 11 pages, 3 figures, to appear in J. reine angew. Math

arxiv created 1998/09/29 · arxiv updated 2009/11/30

Abstract

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) x Q)=0, where r_m denotes the m-th level of the rank filtration.

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