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We give a proof of Pixton's generalized Faber-Zagier relations in thetautological Chow ring of $\overline M_{g,n}$. The strategy is very similar tothe work of Pandharipande-Pixton-Zvonkine, who have given a proof of the sameresult in cohomology. The main tool is the Givental-Teleman classification ofsemisimple cohomological field theories, which, while in general only known incohomology, via virtual localization can be shown to be also valid in Chow forthe equivariant Gromov-Witten theory of the projective line. We obtain therelations just from this theory.

Relations on $\overline M_{g,n}$ via equivariant Gromov-Witten theory of $\mathbb P^1$