On the K-theory of elliptic curves
K-Theory and Homology
2007-05-23 v1 Algebraic Geometry
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_*(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.
Cite
@article{arxiv.math/9809173,
title = {On the K-theory of elliptic curves},
author = {Kevin P. Knudson},
journal= {arXiv preprint arXiv:math/9809173},
year = {2007}
}
Comments
11 pages, 3 figures, to appear in J. reine angew. Math