Geodesic
Vanishing of Brauer groups of moduli stacks of stable curves
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e115

Voir la notice de l'article provenant de la source Cambridge University Press

We show that the cohomological Brauer groups of the moduli stacks of stable genus g curves over the integers and an algebraic closure of the rational numbers vanish for any $g\geq 2$. For the n marked version, we show the same vanishing result in the range $(g,n)=(1,n)$ with $1\leq n \leq 6$ and all $(g,n)$ with $g\geq 4.$ We also discuss several finiteness results on cohomological Brauer groups of proper and smooth Deligne-Mumford stacks over the integers. 
Bartling, Sebastian; Ito, Kazuhiro. Vanishing of Brauer groups of moduli stacks of stable curves. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e115. doi: 10.1017/fms.2025.10076
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