Shimura varieties and \(\lambda\)-adic representations. (English) Zbl 0743.14019

Kottwitz, Robert E.

Automorphic forms, Shimura varieties, and L-functions. Vol. I, Proc. Conf., Ann Arbor/MI (USA) 1988, Perspect. Math. 10, 161-209 (1990).

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[For the entire collection see Zbl 0684.00003.]
This paper discusses Hasse-Weil zeta-functions of Shimura varieties from the point of view of endoscopy and the stable trace formula.

Reviewer: R.E.Kottwitz (Seattle)

MSC:

11G18	Arithmetic aspects of modular and Shimura varieties
11F70	Representation-theoretic methods; automorphic representations over local and global fields
11R39	Langlands-Weil conjectures, nonabelian class field theory
11F72	Spectral theory; trace formulas (e.g., that of Selberg)
14G10	Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)

Keywords:

Hasse-Weil zeta-functions of Shimura varieties; endoscopy; stable trace formula