Additive decompositions for rings of modular forms

Lennart Meier

doi:10.4171/dm/874

Additive decompositions for rings of modular forms

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for SL
2

Z. 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.

Original language	English
Pages (from-to)	427-488
Journal	Documenta Mathematica
Volume	27
DOIs	https://doi.org/10.4171/dm/874
Publication status	Published - 1 Jan 2022

Keywords

modular forms
moduli stacks of elliptic curves
Cohen-Macaulay

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AB - We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for SL 2 Z. 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.

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KW - moduli stacks of elliptic curves

KW - Cohen-Macaulay

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VL - 27

SP - 427

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JO - Documenta Mathematica

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ER -

Additive decompositions for rings of modular forms

Abstract

Keywords

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