The local symbol complex of a Reciprocity Functor

Abstract

For a reciprocity functor $\mathcal{M}$ we consider the local symbol complex $\mathcal{M}{\otimes }^M{\mathbb{G}}_m({\eta }_C)\to {\oplus }_{P\in C}\mathcal{M}(k)\to \mathcal{M}(k)$, 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 conditions, then the homology of the above complex is isomorphic to the $K$-group of reciprocity functors $T(\mathcal{M},{\underline{CH}}_0(C{)}^0)(Speck)$.

arXiv comment17 pages

References in corpus (1)

• Voevodsky's motives and Weil reciprocity