Twisted Lefschetz number formula and 𝑝-adic trace formula

Xiang, Zhengyu

doi:10.1090/tran/7522

Twisted Lefschetz number formula and $p$-adic trace formula
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Trans. Amer. Math. Soc. 371 (2019), 5787-5821 Request permission

Abstract:

For a reductive group $G_{/\mathbb {Q}}$, we interpolate Arthurs $L^2$-Lefschetz number formula $p$-adically and give a geometric expansion of Urbans $p$-adic trace formula on overconvergent cuspidal representations. If $G_{/\mathbb {Q}}$ is anisotropic at infinity and $H$ is a Weil restriction of $G$, we give a twisted version of Arthur’s $L^2$-Lefschetz number formula for $H$, and we set up both the spectral side and the geometric side of a twisted $p$-adic trace formula for $H$.

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