# Totaro's Question for Adjoint Groups of Types A_{1} and A_{2n}

## TL;DR

This paper affirms Totaro's question for certain classical adjoint groups of types A1 and A2n over fields with characteristic not equal to 2, linking zero-cycles to étale points.

## Contribution

It provides an affirmative answer to Totaro's question specifically for absolutely simple classical adjoint groups of types A1 and A2n in characteristic not 2.

## Key findings

- Confirmed Totaro's question for types A1 and A2n
- Established existence of étale points dividing zero-cycle degrees
- Focused on groups over fields with characteristic ≠ 2

## Abstract

Let $G$ be a smooth connected linear algebraic group over a field $k$, and let $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d \geq 1$, then does $X$ have a closed \'etale point of degree dividing $d$? We give an affirmative answer for absolutely simple classical adjoint groups of types $A_{1}$ and $A_{2n}$ over fields of characteristic $\neq 2$.