|DATE||February 22 (Thu), 2018|
|TITLE||[GS-NT] Hasse-Weil zeta functions of modular curves: introduction to Langlands-Kottwitz-Scholze method 3|
|ABSTRACT||We explain P. Scholze's proof (IMRN 2010), extending the Langlands-Kottwitz method to bad reductions, of the (already estalbished) conjecture
that the Hasse-Weil zeta functions of modular curves $X(N)$ is a product of automorphic L-functions on $GL_2$. A new contribution is certain explicit computatons concerning the semi-simple trace of Frobenius on nearby cycle sheaves.