Stably A1-connected varieties and universal CH0

We study the relationship between several notions of connectedness arising in A1-homotopy theory of smooth schemes over a field k: A1-connectedness, stable A1-connectedness and motivic connectedness, and we discuss the relationship between these notations and rationality properties of algebraic varieties. Motivically connected smooth proper k-varieties are precisely those with “universally trivial” CH0. We show that stable A1-connectedness coincides with motivic connectedness, under suitable hypotheses on k. Then, we observe that there exist stably A1-connected smooth proper varieties over the field of complex numbers that are not A1-connected.