On the second K-group of an elliptic curve

On the second rational K -group of an elliptic curve over global fields of positive characteristic

“…The analogue of Corollary 1.2 over number fields is that the rational rank of the K-group is greater than or equal to |S| + [k : Q] (see [39,Section 1.2,p. 62]).…”

On the K-theory of elliptic curves

“…It is not known for a single curve if K 2 (E) Q is finite dimensional. Beilinson has conjectured that the dimension of this space is related to special values of L-functions on E. This conjecture was modified by Bloch and Grayson [3] to predict that the dimension is the number of infinite places of k plus the number of primes p ⊂ O k where E has split multiplicative reduction modulo p. For a discussion of this see, for example, [10].…”

“…A. Beilinson [1] generalized this construction and made a number of conjectures relating the dimension of K 2 ⊗ Q with the values of L-functions on the curve. More recently, Goncharov-Levin [6], Rolshausen-Schappacher [10], and Wildeshaus [15] have made further progress in this area.…”

OnK2of Certain Families of Curves

“…That K T 2 (C) int is finitely generated is only known if g = 0. Most of the work on the conjecture has been put into constructing r independent elements in K T 2 (C) int / torsion and, if possible, relating the resulting regulator with the L-value either numerically or theoretically (see, e.g., [10,11,20,13,17,18,12,16]).…”