Geodesic
Motivic Steenrod operations in characteristic p
Forum of Mathematics, Sigma, Tome 8 (2020)

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For a prime p and a field k of characteristic $p,$ we define Steenrod operations $P^{n}_{k}$ on motivic cohomology with $\mathbb {F}_{p}$-coefficients of smooth varieties defined over the base field $k.$ We show that $P^{n}_{k}$ is the pth power on $H^{2n,n}(-,\mathbb {F}_{p}) \cong CH^{n}(-)/p$ and prove an instability result for the operations. Restricted to mod p Chow groups, we show that the operations satisfy the expected Adem relations and Cartan formula. Using these new operations, we remove previous restrictions on the characteristic of the base field for Rost’s degree formula. Over a base field of characteristic $2,$ we obtain new results on quadratic forms. 
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     author = {Eric Primozic},
     title = {Motivic {Steenrod} operations in characteristic p},
     journal = {Forum of Mathematics, Sigma},
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     year = {2020},
     doi = {10.1017/fms.2020.34},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.34/}
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Eric Primozic. Motivic Steenrod operations in characteristic p. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.34

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