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arXiv · 2609.10140

Frobenius--Cartier duality via lax equalizers

Fei Ren
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Abstract

We prove a duality theorem for lax equalizers of stable $\infty$-categories, and we apply it to Frobenius and Cartier modules on a Noetherian $F$-finite scheme $X$ of characteristic $p$ with a unit dualizing complex. When $X$ has affine diagonal, comparison with the derived categories of coherent modules and passage to homotopy categories recovers Baudin's derived Hom duality. The duality of coherent modules exchanges the standard $t$-structure on one side with the perverse $t$-structure determined by the dualizing complex on the other. In particular, it identifies the abelian category of coherent Cartier modules with a perverse heart of coherent Frobenius modules, and conversely.

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Fei Ren. 2026-09-09. Frobenius--Cartier duality via lax equalizers. https://arxiv.org/abs/2609.10140

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