Strong-cycle formula for the Chow pushforward on smooth Artin stacks

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Let π ⁣:X→X\pi\colon\mathcal {X}\to{\mathbf X} be a good moduli space map from a properly stable smooth Artin stack. Let eZe_\mathcal {Z} be the generic stabilizer order of a strong cycle Z\mathcal {Z}. Strong-cycle pushforward formula. The pushforward map

π∗ ⁣:A∗(X)Q→A∗(X)Q\pi_*\colon A^*(\mathcal {X})_\mathbb{Q}\to A^*({\mathbf X})_\mathbb{Q}

defined in the cited theorem satisfies

π∗[Z]=eZ−1[π(Z)]\pi_*[\mathcal {Z}]=e_\mathcal {Z}^{-1}[\pi(\mathcal {Z})]

for every strong cycle Z\mathcal {Z}. The claim is known for strong zero-cycles and for smooth strong substacks, but remains conjectural for general strong cycles.

References

Primary source

Dan Edidin and Matthew Satriano, “Strong cycles and intersection products on good moduli spaces”, arXiv:1609.08162 (2016).

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