The cohomology of the moduli space of curves at infinite level
Full level-n structures on smooth, complex curves are trivializations of the n-torsion points of their Jacobians. We give an algebraic proof that the etale cohomology of the moduli space of smooth, complex curves of genus at least 2 with "infinite level structure" vanishes in degrees above...
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext bestellen |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | Full level-n structures on smooth, complex curves are trivializations of the
n-torsion points of their Jacobians. We give an algebraic proof that the etale
cohomology of the moduli space of smooth, complex curves of genus at least 2
with "infinite level structure" vanishes in degrees above 4g-5. This yields a
new perspective on a result of Harer who showed such vanishing already at
finite level via topological methods. We obtain similar results for moduli
spaces of stable curves and curves of compact type which are not covered by
Harer's methods. The key ingredients in the proof are a vanishing statement for
certain constructible sheaves on perfectoid spaces and a comparison of the
etale cohomology of different towers of Deligne-Mumford stacks in the presence
of ramification. |
---|---|
DOI: | 10.48550/arxiv.1911.07392 |