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

• Lennart Meier ^[1] ; Viktoriya Ozornova ^[2]
  1. [1] Utrecht University

     Utrecht University

     Países Bajos

     
  2. [2] Ruhr University Bochum

     Ruhr University Bochum

     Kreisfreie Stadt Bochum, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 1, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-019-0532-5
• Enlaces
  • Texto completo
• Resumen

  • Among topological modular forms with level structure, TMF0(7) at the prime 3 is the first example that had not been understood yet. We provide a splitting of TMF0(7) at the prime 3 as TMF-module into two shifted copies of TMF and two shifted copies of TMF1(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.