Geodesic
Additive decompositions for rings of modular forms
Documenta mathematica, Tome 27 (2022), pp. 427-488.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for $SL_2\mathbb{Z}$. 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.
Classification : 11F11, 14D23
Keywords: modular forms, moduli stacks of elliptic curves, Cohen-Macaulay 
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     author = {Meier, Lennart},
     title = {Additive decompositions for rings of modular forms},
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Meier, Lennart. Additive decompositions for rings of modular forms. Documenta mathematica, Tome 27 (2022), pp. 427-488. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a57/