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The Brauer groups of moduli of genus three curves, abelian threefolds and plane curves

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Andrea Di Lorenzo, Roberto Pirisi

Algebraic Geometry · Submitted 9 Feb 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We compute the $\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree $d$ over any algebraically closed field of characteristic different from two, three and coprime to $d$.

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arXiv ID2402.06620 (version 2)
Pith IDQYB4VWZQ, Pith's permanent record of this paper and its review
CitationAndrea Di Lorenzo, Roberto Pirisi. "The Brauer groups of moduli of genus three curves, abelian threefolds and plane curves." arXiv:2402.06620 (2024). https://pith.science/paper/QYB4VWZQ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,080 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.75 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.04 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We compute the $\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree $d$ over any algebraically closed field of characteristic different from two, three and coprime to $d$. We achieve this result by computing the low degree cohomological invariants of these stacks. As a corollary we are additionally able to compute the $\ell$-primary torsion of the Brauer group of the moduli stack of principally polarized abelian varieties of dimension three over any field of characteristic different from two.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We compute the $\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree $d$ over any algebraically closed field of characteristic different from two, three and coprime to $d$. result 0.81 0.95 0.91 asserted 1.00
s1 We achieve this result by computing the low degree cohomological invariants of these stacks. method 1.00 0.92 0.04 asserted 1.00
s2 As a corollary we are additionally able to compute the $\ell$-primary torsion of the Brauer group of the moduli stack of principally polarized abelian varieties of dimension three over any field of characteristic different from two. result 1.00 0.95 0.15 asserted 0.99

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Original abstract

We compute the $\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree $d$ over any algebraically closed field of characteristic different from two, three and coprime to $d$. We achieve this result by computing the low degree cohomological invariants of these stacks. As a corollary we are additionally able to compute the $\ell$-primary torsion of the Brauer group of the moduli stack of principally polarized abelian varieties of dimension three over any field of characteristic different from two.

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