21 citations · 26 across the 8 of their papers we have counts for
9 papers
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…
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 +…
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…
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…
The motivic structures and in the cohomology of moduli spaces of curves
Samir Canning, Hannah Larson, Sam Payne +1
We study the appearances of and in the weight-graded compactly supported cohomology of moduli spaces of curves. As applications, we prove new n…
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…
Hopf algebras in the cohomology of , , and
Francis Brown, Melody Chan, Søren Galatius +1
We describe a bigraded cocommutative Hopf algebra structure on the weight zero compactly supported rational cohomology of the moduli space of principally polarized abelian varietie…
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 and show that this can be computed as the cohomology of a…
The tropicalization of the moduli space of curves II: Topology and applications
Melody Chan, Soren Galatius, Sam Payne
We study the topology of the tropical moduli space parametrizing stable tropical curves of genus g with n marked points in which the bounded edges have total length 1, and prove th…