3 papers
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…
math.AG2026
Moduli spaces of curves with polynomial point counts
Samir Canning, Hannah Larson, Sam Payne +1
We prove that the number of curves of a fixed genus g over finite fields is a polynomial function of the size of the field if and only if g is at most 8. Furthermore, we determine…
math.AG2025
FA-modules of holomorphic forms on
Samir Canning, Hannah Larson, Sam Payne +1
For fixed genus g and varying finite marking set A, the gluing and forgetful maps give the spaces of holomorphic forms on the moduli space of stable A-marked curves of genus g has…