The symplectic period of certain Eisenstein series on GL(2n+1) matches the L-function ratio predicted by relative Langlands duality, confirming the dual pair Sp(2n)\GL(2n+1) and GL(n)xGL(n+1)\GL(2n+1) in the tested cases.
Enhanced adic formalism and perverse t-structures for higher Artin stacks
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abstract
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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On the relative Langlands duality for $\operatorname{Sp}_{2n} \backslash \operatorname{GL}_{2n+1}$ (with an appendix by Zeyu Wang)
The symplectic period of certain Eisenstein series on GL(2n+1) matches the L-function ratio predicted by relative Langlands duality, confirming the dual pair Sp(2n)\GL(2n+1) and GL(n)xGL(n+1)\GL(2n+1) in the tested cases.