Operations in étale and motivic cohomology

Guillou, Bert; Weibel, Chuck

doi:10.1090/tran/7657

Operations in étale and motivic cohomology
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by Bert Guillou and Chuck Weibel PDF

Trans. Amer. Math. Soc. 372 (2019), 1057-1090 Request permission

Abstract:

We classify all étale cohomology operations on $H_{\operatorname {et}}^n(-,\mu _\ell ^{\otimes i})$, showing that they were all constructed by Epstein. We also construct operations $P^a$ on the mod-$\ell$ 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.

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