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arXiv · 1504.08277

The local symbol complex of a Reciprocity Functor

Evangelia Gazaki
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Abstract

For a reciprocity functor $\mathcal{M}$ we consider the local symbol complex $\mathcal{M}\otimes^{M}\mathbb{G}_{m}(η_{C})\to\oplus_{P\in C}\mathcal{M}(k)\to\mathcal{M}(k)$, where $C$ is a smooth complete curve over an algebraically closed field $k$ with generic point $η_{C}$ 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 $T(\mathcal{M},\underline{CH}_{0}(C)^{0})(Spec k)$.

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Evangelia Gazaki. 2015-08-12. The local symbol complex of a Reciprocity Functor. https://doi.org/10.2140/akt.2016.1.317

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