PreprintCC BY 4.0arXiv
Frobenius--Cartier duality via lax equalizers
Abstract
We prove a duality theorem for lax equalizers of stable ∞-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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- Bethe Cycles, Frobenius Identities, and Quantum/Classical Duality
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BibTeX
@misc{ren2026frobeniuscartier,
title = {{Frobenius--Cartier duality via lax equalizers}},
author = {Fei Ren},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10140},
eprint = {2609.10140},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10140},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Frobenius--Cartier duality via lax equalizers
AU - Fei Ren
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10140
UR - https://arxiv.org/abs/2609.10140
AB - We prove a duality theorem for lax equalizers of stable ∞-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.
ER -