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.



Good references for K-theory of modular curves?
I wouldn't recommend Beilinson's 1985 paper as a general reference -- it's terrifyingly compressed, developing an entire new subject in a single short paper, and crashes through the necessary material on modular curves in a couple of sentences.


A much gentler reference would be Flach's 1992 Inventiones paper "A finiteness theorem for the symmetric square of an elliptic curve", which gives a much fuller introduction to K-groups, Gersten complexes, regulator maps etc. You could also try looking at parts of my paper with Lei and Zerbes "Euler systems for Rankin--Selberg convolutions" for more on this. 


