# Cycles on curves and Jacobians: a tale of two tautological rings

@inproceedings{Yin2014CyclesOC,
title={Cycles on curves and Jacobians: a tale of two tautological rings},
author={Qizheng Yin},
year={2014}
}
We connect two notions of tautological ring: one for the moduli space of curves (after Mumford, Faber, etc.), and the other for the Jacobian of a curve (after Beauville, Polishchuk, etc.). The motivic Lefschetz decomposition on the Jacobian side produces relations between tautological classes, leading to results about Faber’s Gorenstein conjecture on the curve side. We also relate certain Gorenstein properties on both sides and verify them for small genera. Further, we raise the question…
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