Modular symbols with values in Beilinson-Kato distributions
Files
First author draft
Date
2023-11-27
Authors
Stevens, Glenn
Busuioc, Cecilia
Version
First author draft
OA Version
Citation
G. Stevens, C. Busuioc. "Modular Symbols with values in Beilinson-Kato Distributions" Transactions of the American Mathematical Society.
Abstract
For each integer nā„1, we construct a GLn(ā)-invariant modular symbol š_n with coefficients in a space of distributions that takes values in the Milnor K_n-group of the modular function field. The Siegel distribution Ī¼ on ā2, with values in the modular function field, serves as the building block for š_n; we define š_n essentially by taking the n-Steinberg product of Ī¼. The most non-trivial part of this construction is the cocycle property of š_n; we prove it by using an induction on n based on the first two cases š_1 and š_2; the first case is trivial, and the second case essentially follows from the fact that Beilinson-Kato elements in the Milnor K_2-group modulo torsion satisfy the Manin relations.