What is the definition of $E_\infty$-operad in the category of chain complexes over $\mathbb{Z}/p\mathbb{Z}$? J. Smith in http://arxiv.org/abs/math/0004003 define it for complexes over $\mathbb{Z}$ (Definition 2.24). Sorry but I'm confused with how does the version in $\mathbb{Z}/p\mathbb{Z}$ must looks like. Thanks!
Given the prominent role of $E_{\infty}$-operads in algebraic topology it seems right to add this tag to the question (and, in particular, the paper quoted in the question is an algebraic topology paper).