Unstable operations in \'etale and motivic cohomology

We classify all 'etale cohomology operations on $H_{\text{et}}^n(-,\text{muell}i)$, showing that they were all constructed by Epstein. We also construct operations $P^a$ on the mod-$\mathrm{\ell }$ motivic cohomology groups $H^{p,q}$, differing from Voevodsky’s operations; we use them to classify all motivic cohomology operations on $H^{p,1}$ and $H^{1,q}$ and suggest a general classification.