Date:
Location:
POT 745
Speaker(s) / Presenter(s):
Luis Sordo Vieira
Artin’s Conjecture for Diagonal Forms
One of Artin’s famous conjectures states that a homogeneous polynomial of the type $a_1x_1^d+\cdots+a_sx_s^d$ over a $p$-adic field $K$ has a nontrivial zero in $K^s$ provided $s>d^2$. The conjecture is known to be true over$\mathbb{Q}_p$ and recently now by collaborative work with David Leep for all unramified extensions of $\mathbb{Q}_p$ with $p>2$. We will talk about the history of Artin’s conjecture and explore some of the known results about Artin’s conjecture on local fields and other fields of interest.
