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arXiv · 2405.17909

$\infty$-Categorical Generalized Langlands Correspondence II: Langlands Program Formalism

Xin Tong
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Abstract

We extend the Langlands program in various subprograms with certain different generalizations: (1) Mixed-parity functorial perturbation of the usual Langlands program after Fargues-Scholze in all characteristics; (2) Robba-Frobenius sheafified functorial perturbation of the usual Langlands program after Fargues-Scholze and Kedlaya-Liu in all characteristics; (3) Arithmetic $D$-module theoretic functorial perturbation of the usual Langlands program after Fargues-Scholze and Abe-Kedlaya-Xu. In certain localized setting we construct Langlands correspondence from smooth representation side to Weil side through geometrized generalized Bernstein center.

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Xin Tong. 2024-05-28. $\infty$-Categorical Generalized Langlands Correspondence II: Langlands Program Formalism. https://arxiv.org/abs/2405.17909

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