On the K-theory of elliptic curves
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 rm denotes the m-th level of the rank filtration.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.