Geodesic
Poincaré polynomial of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$ and the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2017), pp. 20-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain a combinatorial proof that the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$ satisfies the requrrent formula for Poincare polynomials of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$. 
@article{VMUMM_2017_4_a2,
     author = {N. Ya. Amburg and E. M. Kreines and G. B. Shabat},
     title = {Poincar\'e polynomial of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$ and the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {20--27},
     year = {2017},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_4_a2/}
}
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N. Ya. Amburg; E. M. Kreines; G. B. Shabat. Poincaré polynomial of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$ and the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2017), pp. 20-27. http://geodesic.mathdoc.fr/item/VMUMM_2017_4_a2/

[1] Deligne P., “La conjecture de Weil. I”, Publications Mathématiques de l'IHÉS, 43, 1974, 273–307 | DOI | MR

[2] van den Bogaart T., Edixhoven B., “Algebraic stacks whose number of points over finite fields is a polynomial”, Number fields and function fields — two parallel worlds. Progr. Math. Vol. 239. Boston: Birkhauser,, 2005, 39–49 | MR | Zbl

[3] Deligne P., Mumford D., “The irreducibility of the space of curves of given genus”, Publications Mathématiques de l'IHÉS, 36, 1969, 75–109 | DOI | MR | Zbl

[4] Etingof P., Henriques A., Kamnitzer J., Rains E., The cohomology ring of the real locus of the moduli space of stable curves of genus $0$ with marked points, 2005, arXiv: math.AT/0507514 | MR

[5] Getzler E., “Operands and moduli spaces of genus 0 Riemann surfaces”, The Moduli Space of Curves, Progr. Math., 129, Birkhauser, Boston, 1995, 199–230 | MR | Zbl

[6] Bergstrom J., Tommasi O., “The rational cohomology of $\overline{\mathcal{M}_4}$”, Math. Ann., 338:1 (2007), 207–239 | DOI | MR | Zbl

[7] van der Geer G., “Counting curves over finite fields”, Finite Fields and Appl., 32 (2015), 207–232 | DOI | MR | Zbl

[8] Keel S., “Intersection theory of moduli space of stable n-pointed curves of genus zero”, Trans. Amer. Math. Soc., 330:2 (1992), 545–574 | MR | Zbl