2025/03/06 by Jack Morgan Davies, Davies, Jack Morgan, Sil Linskens +1 · 1 citation
Mathematics · Physics and Astronomy · #14A30 #19L47 #55P42 #55P91 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2503.04494
openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The interplay between equivariant stable homotopy theory and spectral algebraic geometry is used to construct a derived Tate curve over KU((q)), a lift of the classical elliptic curve of Tate over Z((q)). Applications of both an algebro-geometric and a topological flavour follow. First, we construct a spectral algebro-geometric model for the compactification of the moduli stack of oriented elliptic curves, giving a canonical choice of holomorphic topological q-expansion map. Then we define globally equivariant forms of Tate K-theory KO((q)) and KU((q)), and equip them with globally equivariant meromorphic topological q-expansion maps from global topological modular forms. Finally, we explore C2-equivariant versions of global Tate K-theory and connect them with C2-equivariant global topological modular forms with level structures.