Just assign the list as the datasource. Also I assume you don't want to reload the list on every PostBack.
protected void Page_Load(object sender, EventArgs e)
{
if (!Page.IsPostBack)
{
List<string> list = new List<string>()
{
"test",
"test2"
};
ShowAssumptions.DataSource = list;
ShowAssumptions.DataBind();
}
}