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Enhanced adic formalism and perverse t-structures for higher Artin stacks

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arxiv 1404.1128 v2 pith:K53LHCH7 submitted 2014-04-04 math.AG

Enhanced adic formalism and perverse t-structures for higher Artin stacks

classification math.AG
keywords adicartincategoriesformalismstacksarxivinftyperverse
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In this sequel of arXiv:1211.5294 and arXiv:1211.5948, we develop an adic formalism for \'etale cohomology of Artin stacks and prove several desired properties including the base change theorem. In addition, we define perverse t-structures on Artin stacks for general perversity, extending Gabber's work on schemes. Our results generalize results of Laszlo and Olsson on adic formalism and middle perversity. We continue to work in the world of $\infty$-categories in the sense of Lurie, by enhancing all the derived categories, functors, and natural transformations to the level of $\infty$-categories.

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    For split almost simple groups over function fields, self-intersections of diagonal cycles on shtuka moduli, with determinant line-bundle insertions, equal higher derivatives of adjoint L-functions.