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math.AG2026
The Prym-Green conjecture in even genera up to 30
Sam Payne, Thomas Willwacher
We prove the Prym-Green conjecture in every even genus from 20 to 30. The genus 24 case disproves the suggestion of Chiodo-Eisenbud-Farkas-Schreyer that the conjecture might fail i…
math.AG2026
Polynomial point counts for moduli spaces of curves with marked points
Sam Payne, Thomas Willwacher
We prove that the number of curves of a fixed genus g with n marked points over finite fields is a polynomial function of the cardinality of the field if and only if g = 0 or 3g +…
math.AG2026
On the Hodge and Tate conjectures for moduli spaces of curves
Sam Payne
We survey recent progress on the cohomology of moduli spaces of stable curves through the lens of the Hodge and Tate conjectures, especially their generalized coniveau forms, which…