2022/11/10 by Kevin Lin, Lin, Kevin · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cohomology #Duality (order theory) #Eisenstein series #FOS: Mathematics #Functor #Geometry and complex manifolds #Mathematics #Modular form #Poincaré duality #Poincaré series #Pure mathematics #Representation Theory (math.RT) #Series (stratigraphy) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.2211.05282
published in arXiv (Cornell University) (Cornell University) · 55 p
arxiv created 2022/11/10 · openalex publication_date 2022/11/10 · arxiv updated 2022/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the setting of global geometric Langlands, we show that miraculous duality on the stack of principal bundles on a curve intertwines the functor of Poincare series with the dual functor to Whittaker coefficients. We construct, for arbitrary parabolic subgroups, Jacquet functors controlling constant terms of Poincare series and Whittaker coefficients of Eisenstein series in local terms.