In topology, Steenrod squares are operations on the mod 2 cohomology of a space. The i-th Steenrod square sends mod 2 cohomology in degree n to mod 2 cohomology in degree n+i. For each prime odd p there are analogues of the Steenrod squares called the p-th operations on mod p cohomology.

Motivic cohomology seems to be the best analogue in algebraic geometry for the topologists´ cohomology groups. Unlike cohomology groups which are graded by degree, motivic cohomology groups are bigraded. The first degree is called the motivic degree and the second is called the simplicial degree. There are also two kinds of cohomology operations. The first are the simplicial operations constructed by Kriz and May. The second are the motivic ones constructed by Voevodsky.

In my talk, I will explain all of this along with a theorem I proved with Roy Joshua comparing the two types of operations. (I will also sketch an independent proof of the result due to Guillou and Weibel.)