Shimura Varieties and Trace Formula Seminar

We report a recent result, due to Clozel-Harris-Labesse, Morel and the speaker, on the previous work of Clozel, Kottwitz, Harris-Taylor and Taylor-Yoshida. There are two main features in our work. One feature, which is also crucial in the other improvements, is the use of the stable trace formula, which became available unconditionally after Ngo (extending Laumon-Ngo) finished the proof of the fundamental lemma. The other feature, which is unique in our approach, is that our work extends Harris-Taylor's method to the endoscopic setting. The key is a general version of the counting point formula for Igusa varieties and stabilize the formula.