Additive decompositions for rings of modular forms
Algebraic Geometry
2023-03-01 v4 Number Theory
Abstract
We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We apply this to characterize which rings of modular forms are Cohen--Macaulay and to prove finite generation results. These theorems are based on decomposition results about vector bundles on the compactified moduli stack of elliptic curves.
Cite
@article{arxiv.1710.03461,
title = {Additive decompositions for rings of modular forms},
author = {Lennart Meier},
journal= {arXiv preprint arXiv:1710.03461},
year = {2023}
}
Comments
Minor changes + new appendix. This article supersedes the algebraic part of arXiv:1609.09264