Skip to main content
2 of 2
+ top level tag (ag.)
Myshkin
  • 17.6k
  • 5
  • 71
  • 137

K-theory of an elliptic curve

Given an elliptic curve $E$ over $\mathbb{Q}$, I have read somewhere (But I can't remember exactly where) that the Beilinson conjecture asserts that: The rank of the albelian group $K_{2}(E)$ (the second algebraic K-theory) is equal to the rank of the abelian group of the rational points $E(\mathbb{Q})$.

Conjecture: $\textrm{rk } K_{2}(E)= \textrm{rk } E(\mathbb{Q})$

Question What are some evidences of such conjecture? Is it verified in some known cases?

symmetry
  • 233
  • 1
  • 5