On the K-theory of Elliptic Curves
نویسنده
چکیده
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.
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