2022/03/30 by Jitendra Bajpai, Bajpai, Jitendra, Mattia Cavicchi +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11F70 #14D07 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT) #Primary:11G40 #Secondary:11F75
paper · pdf · doi:10.48550/arxiv.2203.16435
openalex publication_date 2022/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider certain families of Hecke characters ϕ over a quadratic imaginary field F. According to the Bloch-Beilinson conjectures, the order of vanishing of the L-function L(ϕ,s) at the central point s=-1 should be equal to the dimension of the space of extensions of the Tate motive ℚ(1) by the motive associated with ϕ. In this article, we construct candidates for the corresponding extensions of Hodge structures, assuming that the sign of the functional equation of L(ϕ,s) is -1. This is accomplished through the cohomology of variations of Hodge structures over Picard modular surfaces associated with F and Harder's theory of Eisenstein cohomology. Furthermore, we demonstrate that these extensions are naturally realized within certain biextensions. We outline a program to compute the biextension height and utilize it to establish the non-triviality of these extensions.