# MathCS Seminar

Title: Zero-Cycles on Torsors under Linear Algebraic Groups
Defense: Dissertation
Speaker: Reed Sarney of Emory University
Contact: Reed Sarney, rlgordo@emory.edu
Date: 2017-04-03 at 1:00PM
Venue: W303
Abstract:
Let $k$ be a field, let $G$ be a smooth connected linear algebraic group over $k$, and let $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d$, does $X$ have a closed {\'e}tale point of degree dividing $d$? We give a positive answer in two cases: \begin{enumerate} \item $G$ is an algebraic torus of rank $\leq 2$ and $\textup{ch}(k)$ is arbitrary, and \item $G$ is an absolutely simple adjoint group of type $A_1$ or $A_{2n}$ and $\textup{ch}(k) \neq 2$. \end{enumerate} We also present the first known examples where Totaro's question has a negative answer.