Robert P. Langlands

Author's comments: There are two papers on the Bethe Ansatz, but the work is far from complete. I have always wanted to return not only to the algebraic geometrical arguments initiated in the second paper, which seem to me of considerable intrinsic mathematical interest as algebraic geometry, but also to the notion of Wellenkomplex and the Puiseux expansions introduced briefly at the end of the first paper. So far, I have not found the time.

Author's comments: It has been pointed out by J. Milne, by M. Pfau and by H. Reimann that there is a blunder in this paper in the treatment of gerbes. For a description of the error, for necessary corrections, and for further references, see the notes of Reimann, The semi-simple zeta function of quaternionic Shimura varieties, Lect. Notes Math. 1657.

Author's comments: Although this paper has some merit, it also leaves a lot to be desired, and suffers from the author's inexperience with the material. For a better treatment of more general questions and corrections to the assertions of this paper, the reader is advised to consult a paper of Thomas Zink, Über die schlechte Reduktion einiger Shimuramannigfaltigkeiten, Comp. Math. 45 (1981).