Abstract

For a reciprocity functor $\mathcal{ℳ}$ we consider the local symbol complex

where $C$ is a smooth complete curve over an algebraically closed field $k$ with generic point ${\eta }_C$ and ${\otimes }^M$ is the product of Mackey functors. We prove that if $\mathcal{ℳ}$ satisfies certain assumptions, then the homology of this complex is isomorphic to the $K$-group of reciprocity functors $T\left(\mathcal{ℳ},{\underset{¯}{CH}}_0{\left(C\right)}^0\right)\left(Speck\right)$.

Keywords

Mathematical Subject Classification 2010

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