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

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.Comment: Submitted for publication as part of ICM 201