English

The refined class number formula for Drinfeld modules

Number Theory 2025-12-10 v2

Abstract

Let K/kK/k be a finite Galois extension of global function fields. Let EE be a Drinfeld module over kk. We state and prove an equivariant refinement of Taelman's analogue of the analytic class number formula for (E,K/k)(E,K/k), and derive explicit consequences for the Galois structure of the Taelman class group of EE over KK.

Keywords

Cite

@article{arxiv.2309.17256,
  title  = {The refined class number formula for Drinfeld modules},
  author = {María Inés de Frutos-Fernández and Daniel Macias Castillo and Daniel Martínez Marqués},
  journal= {arXiv preprint arXiv:2309.17256},
  year   = {2025}
}

Comments

Final version, to appear in Compositio Mathematica. 53 pages

R2 v1 2026-06-28T12:36:07.430Z