The Langlands-kottwitz Approach for the Modular Curve

@inproceedings{Scholze2010TheLA,
  title={The Langlands-kottwitz Approach for the Modular Curve},
  author={Peter Scholze},
  year={2010}
}
We show how the Langlands-Kottwitz method can be used to determine the local factors of the Hasse-Weil zeta-function of the modular curve at places of bad reduction. On the way, we prove a conjecture of Haines and Kottwitz in this special case.