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Given a matroid $M$ one can define its Orlik-Solomon algebra $OS(M)$ and theBergman fan $\Sigma_0(M)$. On the other hand to any rational polyhedral fan$\Sigma$ one can associate its tropical homology and cohomology groups$\F_\bullet(\Sigma)$, $\F^\bullet (\Sigma)$. We will show that the projectiveOrlik-Solomon algebra $OS_0(M)$ is canonically isomorphic to $\F^\bullet(\Sigma_0(M))$.

The Orlik-Solomon Algebra and the Bergman Fan of a Matroid