2018/12/11 by Lennart Meier, Meier, Lennart, Viktoriya Ozornova +1 · 1 citation
Mathematics · #11F11 #14D23 #14J15 #55N34 #55P42 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1812.04425
openalex publication_date 2018/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.