Expository survey of when Chow rings and cohomology rings of moduli spaces of curves are tautological and when their point counts over finite fields are polynomials in q.
Burkhardt,Weight 11 Compactly Supported Cohomology of Moduli Spaces of Curves in excess four, 2024, arXiv:2407.16372
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Chow rings, cohomology rings, and point counts of moduli spaces of curves
Expository survey of when Chow rings and cohomology rings of moduli spaces of curves are tautological and when their point counts over finite fields are polynomials in q.