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

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We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for SL2​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.
DOI : 10.4171/dm/874
Classification : 11F11, 14D23
Mots-clés : modular forms, moduli stacks of elliptic curves, Cohen-Macaulay 
Lennart Meier. Additive decompositions for rings of modular forms. Documenta mathematica, Tome 27 (2022), pp. 427-488. doi: 10.4171/dm/874
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     author = {Lennart Meier},
     title = {Additive decompositions for rings of modular forms},
     journal = {Documenta mathematica},
     pages = {427--488},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/874},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/874/}
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