Artin's Conjecture on Zeros of $p$-Adic Forms

TL;DR

This paper reviews the progress on Artin's Conjecture regarding the zeros of p-adic forms, highlighting recent advances in quartic and quadratic systems since 1945.

Contribution

It provides an exposition of various approaches and recent developments related to Artin's Conjecture, focusing on quartic and quadratic forms.

Findings

Progress in understanding zeros of quartic p-adic forms

Advances in systems of quadratic forms

Historical overview of research since 1945

Abstract

This is an exposition of work on Artin's Conjecture on the zeros of $p$-adic forms. A variety of lines of attack are described, going back to 1945. However there is particular emphasis on recent developments concerning quartic forms on the one hand, and systems of quadratic forms on the other.