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arXiv · 2512.24967

Cartier duality for gerbes of vector bundles

Juan Esteban Rodríguez Camargo
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Abstract

We prove a Cartier duality for gerbes of algebraic and analytic vector bundles as an anti-equivalence of Hopf algebras in the category of kernels of analytic stacks. As an application, we prove that the category of solid quasi-coherent sheaves on the Hodge-Tate stack of a smooth rigid variety over an algebraically closed field $C$ of mixed characteristic $(0,p)$ is equivalent to the category of weight $1$ sheaves on Bhatt-Zhang's Simpson gerbe.

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Juan Esteban Rodríguez Camargo. 2025-12-31. Cartier duality for gerbes of vector bundles. https://arxiv.org/abs/2512.24967

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