| Autor: |
Samir Canning, Hannah Larson, Sam Payne |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
Forum of Mathematics, Sigma, Vol 11 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2050-5094 |
| DOI: |
10.1017/fms.2023.59 |
| Popis: |
We prove that the rational cohomology group $H^{11}(\overline {\mathcal {M}}_{g,n})$ vanishes unless $g = 1$ and $n \geq 11$ . We show furthermore that $H^k(\overline {\mathcal {M}}_{g,n})$ is pure Hodge–Tate for all even $k \leq 12$ and deduce that $\# \overline {\mathcal {M}}_{g,n}(\mathbb {F}_q)$ is surprisingly well approximated by a polynomial in q. In addition, we use $H^{11}(\overline {\mathcal {M}}_{1,11})$ and its image under Gysin push-forward for tautological maps to produce many new examples of moduli spaces of stable curves with nonvanishing odd cohomology and nontautological algebraic cycle classes in Chow cohomology. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
