Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Ren, Fei
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212191621