Meromorphic vector bundles on the Fargues–Fontaine curve

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 \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.

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BibTeX RIS

BibTeX

@article{gleason2026meromorphic,
  title = {{Meromorphic vector bundles on the Fargues–Fontaine curve}},
  author = {Ian Gleason and Alexander B. Ivanov and Felix Zillinger},
  journal = {Journal of the European Mathematical Society},
  year = {2026},
  month = may,
  doi = {10.4171/jems/1789},
  url = {https://doi.org/10.4171/jems/1789},
  note = {CC BY},
}

RIS

TY  - JOUR
TI  - Meromorphic vector bundles on the Fargues–Fontaine curve
AU  - Ian Gleason
AU  - Alexander B. Ivanov
AU  - Felix Zillinger
PY  - 2026
DA  - 2026/05/21
JO  - Journal of the European Mathematical Society
DO  - 10.4171/jems/1789
UR  - https://doi.org/10.4171/jems/1789
AB  - 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.
SN  - 1435-9855
SN  - 1435-9863
ER  -

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