On successive minimal bases of division points of Drinfeld modules

2023/04/06 by Maozhou Huang, Huang, Maozhou
Mathematics · #11G09 #11S15 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2304.02854

openalex publication_date 2023/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define successive minimal bases (SMBs) for the space of uⁿ-division points of a Drinfeld \mathbbF_q[t]-module over a local field, where u is a finite prime of \mathbbF_q[t] and n is a positive integer. These SMBs share similar properties to those of SMBs of the lattices associated to Drinfeld modules. We study the relations between these SMBs and those of the lattices. Finally, we apply the relations to study the explicit wild ramification subgroup action on an SMB of the space of uⁿ-division points and show the function field analogue of Szpiro's conjecture for rank 2 Drinfeld modules under a certain limited situation.

Related

• Drinfeld modules, Frobenius endomorphisms, and CM-liftings
• Ramification of Tate modules for rank 2 Drinfeld modules
• Kummer theory of division points over Drinfeld modules of rank one
• Siegel's theorem for Drinfeld modules
• On the torsion of Drinfeld modules of rank two