2023/11/24 by Cecilia Busuioc, Busuioc, Cecilia, Jeehoon Park +5 · 1 citation
Mathematics · #14F67 (Primary) 19D45 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2311.14620
openalex publication_date 2023/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
For each integer n≥ 1, we construct a GLn(\mathbb Q)-invariant modular symbol \bmξn with coefficients in a space of distributions that takes values in the Milnor Kn-group of the modular function field. The Siegel distribution \bmμ on \mathbb Q2, with values in the modular function field, serves as the building block for \bmξn; we define \bmξn essentially by taking the n-Steinberg product of \bmμ. The most non-trivial part of this construction is the cocycle property of \bmξn; we prove it by using an induction on n based on the first two cases \bmξ1 and \bmξ2; the first case is trivial, and the second case essentially follows from the fact that Beilinson-Kato elements in the Milnor K2-group modulo torsion satisfy the Manin relations.