A pairing on the cuspidal eigenvariety for GSp_2g and the ramification locus

2020/05/10 by Ju-Feng Wu, Wu, Ju-Feng
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2005.04776

openalex publication_date 2020/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we first construct a pairing on the space of analytic distributions associated with GSp_2g. By considering the overconvergent parabolic cohomology groups and following the work of Johansson--Newton, we construct the cuspidal eigenvariety for GSp_2g. The pairing on the analytic distributions then induces a pairing on some coherent sheaves of the cuspidal eigenvariety. As an application, we follow the strategy of Bellaïche to study the ramification locus of the cuspidal eigenvariety over the corresponding weight space.

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