Drinfeld modular polynomials in higher rank II: Kronecker congruences

作者：Breuer Florian^*; Rueck Hans Georg

来源：Journal of Number Theory, 2016, 165: 1-14.

DOI：10.1016/j.jnt.2016.01.001

• Drinfeld modules
• Modular polynomials
• Isogenies
• Isomorphism invariants

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 F-q [T]-modules of rank r >= 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].

• 出版日期2016-8