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In this article, we develop a theory of Grothendieck's six operations forderived categories in \'etale cohomology of Artin stacks. We prove severaldesired properties of the operations, including the base change theorem inderived categories. This extends all previous theories on this subject,including the recent one developed by Laszlo and Olsson, in which theoperations are subject to more assumptions and the base change isomorphism isonly constructed on the level of sheaves. Moreover, our theory works for higherArtin stacks as well.  Our method differs from all previous approaches, as we exploit the theory ofstable $\infty$-categories developed by Lurie. We enhance derived categories,functors, and natural isomorphisms to the level of $\infty$-categories andintroduce $\infty$-categorical (co)homological descent. To handle the "homotopycoherence", we apply the results of our previous article arXiv:1211.5294 anddevelop several other $\infty$-categorical techniques.

Enhanced six operations and base change theorem for higher Artin stacks