The high-dimensional cohomology of the moduli space of curves with level structures

Neil J. Fullarton; Andrew Putman

doi:10.4171/jems/945

JournalsjemsVol. 22, No. 4pp. 1261–1287

The high-dimensional cohomology of the moduli space of curves with level structures

Neil J. Fullarton
Rice University, Houston, USA
Andrew Putman
University of Notre Dame, USA

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Abstract

We prove that the moduli space of curves with level structures has an enormous amount of rational cohomology in its cohomological dimension. As an application, we prove that the coherent cohomological dimension of the moduli space of curves is at least $g -2$ . Well known conjectures of Looijenga would imply that this is sharp.

Cite this article

Neil J. Fullarton, Andrew Putman, The high-dimensional cohomology of the moduli space of curves with level structures. J. Eur. Math. Soc. 22 (2020), no. 4, pp. 1261–1287

DOI 10.4171/JEMS/945