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This paper is the third in a series of four papers aiming to describe the(almost integral) Chow ring of $\overline{\mathcal{M}}_3$, the moduli stack ofstable curves of genus $3$. In this paper, we compute the Chow ring of$\widetilde{\mathcal{M}}_3^7$ with $\mathbb{Z}[1/6]$-coefficients.

The (almost) integral Chow ring of $\widetilde{\mathcal{M}}_3^7$