The cohomology of moduli of curves at infinite level
HARVARD-MIT ALGEBRAIC GEOMETRY
Emanuel Reinecke - IAS
Moduli spaces of curves admit finite covers by moduli spaces which parametrize curves together with so-called level structures. In my talk, I will discuss how the cohomology of these spaces at infinite level is related to a profinite property of the mapping class group. I will then explain why tools from p-adic geometry yield vanishing statements for these cohomologies in high degree.