 
Summary: A STABLE TRACE FORMULA III. PROOF OF THE MAIN THEOREMS
James Arthur*
Contents
Introduction
§1 The induction hypotheses
§2 Application to endoscopic and stable expansions
§3 Cancellation of padic singularities
§4 Separation by infinitesimal character
§5 Elimination of restrictions on f
§6 Local trace formulas
§7 Local Theorem 1
§8 Weak approximation
§9 Global Theorems 1 and 2
§10 Concluding remarks
* Supported in part by NSERC Operating Grant A3483.
1
Introduction
This paper is the last of three articles designed to stabilize the trace formula. Our
goal is to stabilize the global trace formula for a general connected group, subject to a
condition on the fundamental lemma that has been established in some special cases. In
