Rings of modular forms and a splitting of TMF0(7)

Lennart Meier, Viktoriya Ozornova

Research output: Contribution to journalArticleAcademic


Among topological modular forms with level structure, {{\,\mathrm{TMF}\,}}_0(7) at the prime 3 is the first example that had not been understood yet. We provide a splitting of {{\,\mathrm{TMF}\,}}_0(7) at the prime 3 as {{\,\mathrm{TMF}\,}}-module into two shifted copies of {{\,\mathrm{TMF}\,}} and two shifted copies of {{\,\mathrm{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.
Original languageEnglish
Article number7
Number of pages73
JournalSelecta Mathematica, New Series
Issue number7
Publication statusPublished - 8 Jan 2020


  • math.AT
  • math.AG
  • 55N34, 55P42, 14J15, 11F11, 14D23


Dive into the research topics of 'Rings of modular forms and a splitting of TMF0(7)'. Together they form a unique fingerprint.

Cite this