I work in algebraic geometry. Lately, the answer to most of my questions seems to be "you should read Lurie's *Higher Algebra*." I took this advice seriously, however it turned out not to be an easy task.

From what I gather, I should learn how to work with $E_\infty$-rings. I understand the definition of a symmetric monoidal $\infty$-category as a certain coCartesian fibration $p\colon C^\otimes \to N({\rm Fin}_*)$, and that an $E_\infty$-ring in a stable symmetric monoidal $\infty$-category $C$ should be a certain section of $p$.

In *Higher Algebra*, $E_\infty$-algebras are a special case of algebras over $\infty$-operads, where the operad ${\rm Comm}$ is just the identity $N({\rm Fin}_*)\to N({\rm Fin}_*)$. Lurie treats general $\infty$-operads in detail in two chapters of about 150 pages each, and in later chapters he specializes to the case of the operads $E_k$. Since I seem to be interested in the final operad ${\rm Comm}$ only, it is difficult for me to motivate myself to read through the chapters about the general theory of $\infty$-operads.

Question.As an algebraic geometer interested in making the step from commutative rings to $E_\infty$-rings, should I care about $E_k$-rings for $k<\infty$, or algebras over more general $\infty$-operads? If so, why?

allof the 150 pages. $\endgroup$ – Denis Nardin Mar 29 '18 at 10:47