Twisted Lefschetz number formula and 𝑝-adic trace formula

Abstract

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