Meromorphic vector bundles on the Fargues–Fontaine curve

We introduce and study the stack of meromorphic G -bundles on the Fargues–Fontaine curve. This object defines a correspondence between the Kottwitz stack \mathfrak{B}(G) and \operatorname{Bun}_{G} . We expect it to play a crucial role in defining and studying an analytification functor that compares the scheme-theoretic and analytic versions of the geometric local Langlands categories. Our first main result is the identification of the generic Newton strata of \operatorname{Bun}_{G}^{\operatorname{mer}} with the Fargues–Scholze charts \mathcal{M} . Our second main result is a generalization of Fargues’ theorem in families. We call this the meromorphic comparison theorem . We expect it to play a key role in proving that the analytification functor is fully-faithful. Along the way, we give new proofs of what we call the topological and scheme-theoretic comparison theorems . These say that the topologies of \operatorname{Bun}_{G} and \mathfrak{B}(G) are reversed and that the two stacks take the same values when evaluated on schemes.