6 papers · 1 filter
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…
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…
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…
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…
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…