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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| Format: | Article |
| Language: | English |
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425100765/type/journal_article |
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| _version_ | 1849320146364006400 |
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| author | Sebastian Bartling Kazuhiro Ito |
| author_facet | Sebastian Bartling Kazuhiro Ito |
| author_sort | Sebastian Bartling |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8bfb6bea87164119bd4fc022b9dac67d |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-8bfb6bea87164119bd4fc022b9dac67d2025-08-20T03:50:12ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.10076Vanishing of Brauer groups of moduli stacks of stable curvesSebastian Bartling0Kazuhiro Ito1https://orcid.org/0000-0002-9613-3128https://ror.org/04mz5ra38 Universität Duisburg-Essen, Fakultät für Mathematik, Thea-Leymann Straße, 45127 Essen, Germany; E-mail:Tohoku University, Mathematical Institute, 6-3, Aoba, Aramaki, Aoba-Ku, Sendai, 980-8578, JapanWe 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.https://www.cambridge.org/core/product/identifier/S2050509425100765/type/journal_article14D2314F2214H10 |
| spellingShingle | Sebastian Bartling Kazuhiro Ito Vanishing of Brauer groups of moduli stacks of stable curves Forum of Mathematics, Sigma 14D23 14F22 14H10 |
| title | Vanishing of Brauer groups of moduli stacks of stable curves |
| title_full | Vanishing of Brauer groups of moduli stacks of stable curves |
| title_fullStr | Vanishing of Brauer groups of moduli stacks of stable curves |
| title_full_unstemmed | Vanishing of Brauer groups of moduli stacks of stable curves |
| title_short | Vanishing of Brauer groups of moduli stacks of stable curves |
| title_sort | vanishing of brauer groups of moduli stacks of stable curves |
| topic | 14D23 14F22 14H10 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425100765/type/journal_article |
| work_keys_str_mv | AT sebastianbartling vanishingofbrauergroupsofmodulistacksofstablecurves AT kazuhiroito vanishingofbrauergroupsofmodulistacksofstablecurves |