On the Formal Carlitz Module

TL;DR

This paper establishes a P-adic class formula for finite extensions of rational function fields over finite fields, extending the theoretical framework in the area of function field arithmetic.

Contribution

It introduces a new P-adic class formula for such extensions, building on and generalizing Taelman's work in the context of function fields.

Findings

Proves a P-adic class formula for finite extensions of rational function fields.

Extends Taelman's work to a broader class of function field extensions.

Provides new tools for understanding arithmetic in function fields.

Abstract

For finite extensions of a rational function field over a finite field, we prove a "P-adic class formula" in the spirit Taelman's work.