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

Autor:	Meier, Lennart, Ozornova, Viktoriya
Rok vydání:	2018
Předmět:	Mathematics - Algebraic Topology Mathematics - Algebraic Geometry 55N34 55P42 14J15 11F11 14D23
Druh dokumentu:	Working Paper
Popis:	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. Comment: 62 pages; one appendix joint with Martin Olbermann
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1812.04425 Zobrazit plný text záznamu View this record from Arxiv