Brauer groups of resolved quiver moduli via gerbes

Pieter Belmans; Gianni Petrella; Sebastián Torres

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arXiv · 2607.06164

Brauer groups of resolved quiver moduli via gerbes

Pieter Belmans·Gianni Petrella·Sebastián Torres

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Abstract

We show that the Brauer group of any resolution of singularities of the moduli space of semistable quiver representations is trivial. We do this by extending the quiver-curve dictionary, translating a proof of the analogous result by Biswas-Hogadi-Holla for moduli of vector bundles on a curve to the setting of moduli of quiver representations, giving an algebro-geometric proof. This gives a new proof of this triviality, first proved by Le Bruyn-Schofield, building on algebraic (resp. cohomological) vanishing results due to Saltman (resp. Colliot-Th\'el\`ene-Sansuc). Reversing the logic, our approach gives a new algebro-geometric proof of these vanishing results.

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BibTeX RIS

Pieter Belmans, Gianni Petrella, Sebastián Torres. 2026-07-07. Brauer groups of resolved quiver moduli via gerbes. https://arxiv.org/abs/2607.06164

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