Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math.,
Oregon State Univ., Corvallis, Ore., 1977), Part 2, pp. 165--184, Proc.
Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979.
Comments
My task at the conference was to explain a proof of Langlands sketched in
a letter to Rapoport. Since I didn't understand Langlands's proof, I instead
found my own proof. My approach is quite different from that of Langlands. The
idea of Langlands for describing the points mod $p$ was to look at them as the
reductions of points in characteristic zero. My idea was to work directly with
the moduli problem in characteristic $p$, and apply the theorems of Honda and
Tate. This idea has been adopted by several later authors (Zink 1981, 1983;
Reimann and Zink 1991; Kottwitz 1992; Harris and Taylor 1999;…). When
Langlands tried to write up his proof for publication, he found errors
1, and
published nothing.
1.
Dieses Resultat wurde in einem Brief von Langlands an Rapoport behauptet. Der Beweis dort,
der auf Methoden von Grothendieck and Messing beruht is aber fehlerhaft.
(These results were asserted in a letter from Langlands to Rapoport. The
proof there, following the methods of Grothendieck and Messing, is however incorrect.)
T. Zink, Math. Nachr. 112 (1983), p.103
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