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

Lennart Meier; Viktoriya Ozornova

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

Algebraic Topology 2018-12-12 v1 Algebraic Geometry

Authors: Lennart Meier , Viktoriya Ozornova

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.

Keywords

topological modular forms tmf0(7) splitting conjecture modular forms elliptic curves moduli stacks

Cite

@article{arxiv.1812.04425,
  title  = {Rings of modular forms and a splitting of $TMF_0(7)$},
  author = {Lennart Meier and Viktoriya Ozornova},
  journal= {arXiv preprint arXiv:1812.04425},
  year   = {2018}
}

Comments

62 pages; one appendix joint with Martin Olbermann

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

Abstract

Keywords

Cite

Comments

Related papers