Twisted Lefschetz number formula and $p$-adic trace formula
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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 $H$.References
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Additional Information
- Zhengyu Xiang
- Affiliation: Shanghai Center for Mathematical Science, Fudan University, Shanghai, China
- MR Author ID: 970829
- Email: xiangzy@fudan.edu.cn
- Received by editor(s): April 10, 2017
- Received by editor(s) in revised form: January 24, 2018
- Published electronically: September 18, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 5787-5821
- MSC (2010): Primary 11E95; Secondary 11E10
- DOI: https://doi.org/10.1090/tran/7522
- MathSciNet review: 3937310