On the K-theory of elliptic curves

Details On the K-theory of elliptic curves On the K-theory of elliptic curves

1998-09-29

arxiv.org/abs/math/9809173v1

J. reine angew. Math. 507 (1999), 81-91

Mathematics

K-Theory and Homology

11 pages, 3 figures, to appear in J. reine angew. Math

Scientific paper

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_*(GL_2(A),Z) in H_*(GL_2(F),Z) coincides with the image of H_*(GL_2(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 r_2(K_2> (A) x Q)=0, where r_m denotes the m-th level of the rank filtration.

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