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

Part of: (Co)homology theory Curves

Published online by Cambridge University Press:  19 September 2025

A. Di Lorenzo Open the ORCID record for A. Di Lorenzo [Opens in a new window]  and
R. Pirisi
A. Di Lorenzo
Affiliation:
Dipartimento di matematica, Università di Pisa, Pisa 56127, Italy andrea.dilorenzo@unipi.it
R. Pirisi
Affiliation:
Dipartimento di matematica e applicazioni ‘R. Caccioppoli’, Università degli Studi di Napoli Federico II, Napoli I-80126, Italy roberto.pirisi@unina.it
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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.

Keywords

Brauer groupsmoduli of curves

MSC classification

Primary: 14F22: Brauer groups of schemes
Secondary: 14H10: Families, moduli (algebraic)

Information

Type
Research Article
Information
Compositio Mathematica , Volume 161 , Issue 7 , July 2025 , pp. 1664 - 1697
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Copyright
© The Author(s), 2025. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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