Additive decompositions for rings of modular forms
Copyright policy )Additive decompositions for rings of modular forms
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.
- Utrecht University Netherlands
moduli stacks of elliptic curves, Mathematics - Algebraic Geometry, Mathematics - Number Theory, FOS: Mathematics, Stacks and moduli problems, modular forms, Number Theory (math.NT), 11F11, Holomorphic modular forms of integral weight, Algebraic Geometry (math.AG), Cohen-Macaulay
moduli stacks of elliptic curves, Mathematics - Algebraic Geometry, Mathematics - Number Theory, FOS: Mathematics, Stacks and moduli problems, modular forms, Number Theory (math.NT), 11F11, Holomorphic modular forms of integral weight, Algebraic Geometry (math.AG), Cohen-Macaulay
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