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arXiv · 1812.04425

Rings of modular forms and a splitting of $TMF_0(7)$

Lennart Meier·Viktoriya Ozornova
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Abstract

Among topological modular forms with level structure, $TMF_0(7)$ at the prime $3$ is the first example that had not been understood yet. We provide a splitting of $TMF_0(7)$ at the prime 3 as $TMF$-module into two shifted copies of $TMF$ and two shifted copies of $TMF_1(2)$. This gives evidence to a much more general splitting conjecture. Along the way, we develop several new results on the algebraic side. For example, we show the normality of rings of modular forms of level $n$ and introduce cubical versions of moduli stacks of elliptic curves with level structure.

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BibTeXRIS

Lennart Meier, Viktoriya Ozornova. 2018-12-11. Rings of modular forms and a splitting of $TMF_0(7)$. https://arxiv.org/abs/1812.04425

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