| Résume | Using the theory of abstract six functor formalisms of analytic stacks, I will explain a general Cartier duality for gerbes of vector bundles in different algebraic and analytic setups. As an application, admitting some foundational aspects of the theory of the analytic Hodge-Tate stack (joint with Anschütz, Le Bras and Scholze), one can deduce a Cartier duality between the categories of quasi-coherent sheaves of (a mild modification of) the analytic Hodge-Tate stack and the Simpson's gerbe of Bhatt-Zhang. |
