On the lower K-groups of an elliptic curve over a global field of positive characteristic

Joint with Seidai Yasuda. We show that the maximal divisible subgroup of groups K1 and K2 of an elliptic curve E over a function field are uniquely divisible. Further, those K-groups modulo this uniquely divisible subgroup are explicitly computed, some cases in terms of the L-values. We also consider motivic cohomology groups of (open) elliptic surfaces over finite fields.