K-Theory of curves over number fields

We consider the algebraic K-groups with coefficients of smooth curves over number fields. We give a proof of the Quillen–Lichtenbaum conjecture at the prime 2 and prove explicit corank formulas for the algebraic K-groups with divisible coefficients. At odd primes these formulas assume the Bloch–Kato conjecture, at the prime 2 the formulas hold nonconjecturally.