2009/09/29 by Takashi Ichikawa, Ichikawa, Takashi
Mathematics · #11F80 #11G18 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11F80 #msc:11G18
paper · pdf · doi:10.48550/arxiv.0909.5277
We correct some errors in the previous version. 19 pages
openalex publication_date 2009/09/29 · arxiv created 2012/02/20 · arxiv updated 2012/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the study of the arithmetic structure of elliptic modular groups which are the fundamental groups of compactified modular curves, these truncated group algebras and their direct sums are considered to construct elliptic modular motives. Our main result is a new theory of Hecke operators on these motives which gives a congruence relation to the Galois action, and their motivic decomposition. Using our Hecke theory, we show that elliptic modular motives are the direct sums of pure motives over certain number fields. This fact implies a kind of algebraicity on iterated Shimura integrals, i.e., multiple L-values of cusp forms of weight 2, and on the periods of modular Ceresa cycles.