For a prime number
p
, we show that differentials
in the motivic cohomology spectral sequence with
p
-local coefficients vanish unless
divides
. We obtain an explicit formula for the first non-trivial differential
, expressing it in terms of motivic Steenrod
p
-power operations and Bockstein maps. To this end, we compute the algebra of operations of
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with
p
-local coefficients. Finally, we construct examples of varieties having non-trivial differentials
in their motivic cohomology spectral sequences.