Here is the list of all my articles on arXiv.

Preprints

1. Meromorphic vector bundles on the Fargues--Fontaine curve (with Alexander Ivanov and Ian Gleason), preprint 2023, submitted
   [ PDF ] [ arXiv ]
   Abstract

   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 \(Bun_G\). 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 BunmerG with the Fargues--Scholze charts M. Our second main result is a generalization of Fargues' theorem in families. We call this the meromorphic comparison 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 topological and schematic comparison theorems. These say that the topologies of \(Bun_G\) and \(\mathfrak{B}(G)\) are reversed and that the two stacks take the same values when evaluated on schemes.