2019/12/08 by Guido Kings, Kings, Guido, Johannes Sprang +1 · 3 citations
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1912.03657
openalex publication_date 2019/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for an arbitrary totally complex number field L the (regularized) critical L-values of algebraic Hecke characters of L divided by certain periods are algebraic integers. This relies on a new construction of an equivariant coherent cohomology class with values in the completion of the Poincaré bundle on an abelian scheme \calA. From this we obtain a cohomology class for the automorphism group of a CM abelian scheme \calA with values in some canonical bundles, which can be explicitly calculated in terms of Eisenstein-Kronecker series. As a further consequence, using an infinitesimal trivialization of the Poincaré bundle, we construct a p-adic measure interpolating the critical L-values in the ordinary case. This generalizes previous results for CM fields by Damerell, Shimura and Katz and settles the algebraicity and p-adic interpolation in the remaining open cases of critical values of Hecke L-functions.