Creating a Generic<T> type instance with a variable containing the Type

Is it possible to achieve the following code? I know it doesn't work, but I'm wondering if there is a workaround?

Type k = typeof(double);
List<k> lst = new List<k>();

Yes, there is:

var genericListType = typeof(List<>);
var specificListType = genericListType.MakeGenericType(typeof(double));
var list = Activator.CreateInstance(specificListType);

A cleaner way might be to use a generic method. Do something like this:

static void AddType<T>()
    where T : DataObject
{
    Indexes.Add(typeof(T), new Dictionary<int, T>());
}