Vanishing of Brauer groups of moduli stacks of stable curves
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425100765/type/journal_article |
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| Summary: | 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. |
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| ISSN: | 2050-5094 |