Acta Mathematica Vietnamica



On the Continuity of the Geometric Side of the Trace Formula
Tobias Finis, Erez Lapid



We extend the geometric side of Arthur’s non-invariant trace formula for a reductive group G defined over Q continuously to a natural space C(G(A)1) of test functions which are not necessarily compactly supported. The analogous result for the spectral side was obtained in [10]. The geometric side is decomposed according to the following equivalence relation on G(Q): γ 1γ 2 if γ 1 and γ 2 are conjugate in G(Q¯) and their semisimple parts are conjugate in G(Q). All terms in the resulting decomposition are continuous linear forms on the space C(G(A)1), and can be approximated (with continuous error terms) by naively truncated integrals.

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