Meromorphic vector bundles on the Fargues--Fontaine curve

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