The refined class number formula for Drinfeld modules

2023/09/29 by de Frutos-Fernández, María Inés, Castillo, Daniel Macias, Marqués, Daniel Martínez
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.17256

Abstract

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

Related

• The refined class number formula for Drinfeld modules
• Iwasawa-type asymptotic formula for Taelman class groups of Drinfeld modules
• Kummer theory of division points over Drinfeld modules of rank one
• Shtuka cohomology and special values of Goss L-functions
• A description of a Drinfeld module with class number h=1 and rank 1