Drinfeld modular polynomials in higher rank II: Kronecker congruences

This is a sequel to the paper [4], in which we introduced Drinfeld modular polynomials of higher rank, using an analytic construction. These polynomials relate the isomorphism invariants of Drinfeld Fq[T]Fq[T]-modules of rank r≥2r≥2 linked by isogenies of a specified type. In the current paper, we give an algebraic construction of greater generality, and prove a generalization of the Kronecker congruences relations, which describe what happens when modular polynomials associated to P-isogenies are reduced modulo a prime P. We also correct an error in [4].