Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrization of the local Langlands correspondence   Following the idea of [Far16], we develop the foundations of the geometric
Langlands program on the Fargues--Fontaine curve. In particular, we define a
category of $\ell$-adic sheaves on the stack $\mathrm{Bun}_G$ of $G$-bundles on
the Fargues--Fontaine curve, prove a geometric Satake equivalence over the
Fargues--Fontaine curve, and study the stack of $L$-parameters. As
applications, we prove finiteness results for the cohomology of local Shimura
varieties and general moduli spaces of local shtukas, and define $L$-parameters
associated with irreducible smooth representations of $G(E)$, a map from the
spectral Bernstein center to the Bernstein center, and the spectral action of
the category of perfect complexes on the stack of $L$-parameters on the
category of $\ell$-adic sheaves on $\mathrm{Bun}_G$.

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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph