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Coherent sheaves on the stack of Langlands parameters
TLDR
In this article, the authors formulate a few conjectures on some hypothetical coherent sheaves on the stacks of arithmetic local Langlands parameters, including their roles played in the local-global compatibility in the Langlands program.Abstract:
We formulate a few conjectures on some hypothetical coherent sheaves on the stacks of arithmetic local Langlands parameters, including their roles played in the local-global compatibility in the Langlands program. We survey some known results as evidences of these conjectures.read more
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Moduli of Langlands Parameters
TL;DR: In this article, a moduli space of Langlands parameters of a nonarchimedean local field of residue characteristic $p was constructed, and it was shown that it is locally of finite type and flat over a closed field of characteristic zero and characteristic p.
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The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support
TL;DR: In this article, the stack of local systems with restricted variation is defined as a geometric object, and a conjecture that makes precise the connection between the category of automorphic sheaves and the space of automomorphic functions is formulated.
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On the derived category of the Iwahori-Hecke algebra
TL;DR: In this article, the derived tensor product with the family of representations interpolating the modified Langlands correspondence over the stack of L-parameters was investigated in the case of the principal block of GL_n.
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Coherent Springer theory and the categorical Deligne-Langlands correspondence
TL;DR: In this article, the Deligne-Langlands conjecture is lifted to the case of the general linear group and the coherent Springer sheaf is realized as a subcategory of coherent sheaves on the stack of unipotent Langlands parameters.
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Automorphic functions as the trace of Frobenius
TL;DR: In this article, it was shown that the Frobenius endofunctor of the category of automorphic sheaves with nilpotent singular support maps isomorphically to the space of unramified automomorphic functions.
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