Sam Payne

activity

20242026

collaborators

5 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 $M_{g, n}$

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…

math.AG2024

The motivic structures $LS_{12}$ and $S_{16}$ in the cohomology of moduli spaces of curves

Samir Canning, Hannah Larson, Sam Payne +1

We study the appearances of $LS_{12}$ and $S_{16}$ in the weight-graded compactly supported cohomology of moduli spaces of curves. As applications, we prove new n…

math.AG2024

Weight two compactly supported cohomology of moduli spaces of curves

Sam Payne, Thomas Willwacher

We study the weight 2 graded piece of the compactly supported rational cohomology of the moduli spaces of curves $M_{g, n}$ and show that this can be computed as the cohomology of a…

On the Hodge and Tate conjectures for moduli spaces of curves

Moduli spaces of curves with polynomial point counts

FA-modules of holomorphic forms on Mg,n​

The motivic structures LS12​ and S16​ in the cohomology of moduli spaces of curves

Weight two compactly supported cohomology of moduli spaces of curves

FA-modules of holomorphic forms on $M_{g, n}$

The motivic structures $LS_{12}$ and $S_{16}$ in the cohomology of moduli spaces of curves