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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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On the K-theory of elliptic curves

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 1999, Issue 507, Pages 81–91, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.1999.507.81, June 2008

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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 r 2 (K 2 (A) ⊗ ℚ) = 0, where rm denotes the mth level of the rank filtration.

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