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.
Conjectural relations in the tautological ring of $\bar{M}_{g,n}$
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abstract
We describe a very large class of conjectural relations in the tautological ring of the moduli space $\bar{M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, extending and generalizing the Faber-Zagier relations. These notes are loosely based on informal talks given by the author at the workshop at KTH Stockholm on "The moduli space of curves and its intersection theory" in April 2012.
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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.