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The Hasse Norm Principle in Global Function Fields

Adelina Mânzăţeanu, Rachel Newton, Ekin Ozman, Nicole Sutherland, Rabia Gülşah Uysal

Abstract

Let $L$ be a finite extension of $\mathbb{F}_q(t)$. We calculate the proportion of polynomials of degree $d$ in $\mathbb{F}_q[t]$ that are everywhere locally norms from $L/\mathbb{F}_q(t)$ which fail to be global norms from $L/\mathbb{F}_q(t)$.

The Hasse Norm Principle in Global Function Fields

Abstract

Let be a finite extension of . We calculate the proportion of polynomials of degree in that are everywhere locally norms from which fail to be global norms from .

Paper Structure

This paper contains 6 sections, 21 theorems, 52 equations.

Table of Contents

  1. Introduction
  2. Reducing to the separable case
  3. Proof of our main results
  4. Class field theory
  5. Constant fields
  6. Proof of Theorem \ref{['thm:main']}

Key Result

Theorem 1.1

We have where the limit is taken over degrees $d$ such that $fh\mid d$.

Theorems & Definitions (34)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 2.1: cohen_odoni
  • Lemma 2.2
  • proof
  • Corollary 2.3
  • proof
  • Corollary 2.4
  • proof
  • ...and 24 more