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arXiv · 2512.13856

Cartier duality via Mittag-Leffler modules

Dima Arinkin·Joshua Mundinger
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Abstract

We construct the Cartier duality equivalence for affine commutative group schemes $G$ whose coordinate ring is a flat Mittag-Leffler module over an arbitrary base ring $R$. The dual $G^\vee$ of $G$ turns out to be an ind-finite ind-scheme over $R$. When $R$ is Noetherian and admits a dualizing complex, we construct a Fourier-Mukai transform between quasicoherent derived categories of $G$ and of $BG^\vee$ and also between those of $G^\vee$ and $BG$.

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Dima Arinkin, Joshua Mundinger. 2025-12-15. Cartier duality via Mittag-Leffler modules. https://arxiv.org/abs/2512.13856

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