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arXiv · 2408.04582

Second adjointness and cuspidal supports at the categorical level

Yuta Takaya
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Abstract

We prove the second adjointness in the setting of the categorical local Langlands correspondence. Moreover, we study the relation between Eisenstein series and cuspidal supports and present a conjectural characterization of irreducible smooth representations with supercuspidal $L$-parameters regarding geometric constant terms. The main technical ingredient is an induction principle for geometric Eisenstein series which allows us to reduce to the situations already treated in the literature.

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Yuta Takaya. 2024-08-08. Second adjointness and cuspidal supports at the categorical level. https://arxiv.org/abs/2408.04582

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