# Good references for K-theory of modular curves?

The title says it. I am looking for a good exposition on the K-theory of the curves $X_{i}(N)$, $Y_{i}(N)$, where $i\in\{0,1\}$. I have some background in $K$-theory and also some background in modular curves.

• Maybe you should specify a little more explicitly what you are looking for. Beilinson's conjectures give a fairly general picture of what is expected of the K-theory (in particular of modular curves). Besides Beilinson's papers on higher regulators for modular curves, there are a couple of expository papers on Beilinson's conjectures by Nekovar, Deninger-Scholl, Schappacher-Scholl, etc. There is quite a follow-up literature on construction of special elements in K-groups, but essentially Beilinson's conjectures remain unproved even in the curve case. – Matthias Wendt Dec 21 '15 at 15:31
• Beilinson's "Higher regulators and values of L-functions", J. Sov. Math. 30 (1985) is supposed to be a good (general) reference here. – jvo Dec 21 '15 at 20:56