A Schanuel Property for $j$

Abstract

I give a model-theoretic setting for the modular $j$ function and its derivatives. These structures, here called $j$-fields, provide an adequate setting for interpreting the Ax-Schanuel theorem for $j$ (Pila-Tsimerman 2015). Following the ideas of M. Bays, J. Kirby and A.J. Wilkie for exponential fields, I prove a generic transcendence property for the $j$ function.

18 pages

References in corpus (1)

• Ax-Schanuel for the j-function

Cited by in corpus (4)

• Blurrings of the $j$-function
• A closure operator respecting the modular $j$-function
• Generic Solutions of Equations Involving the Modular $j$-function
• Hilbert polynomials for finitary matroids