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

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

### 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)

Zbl 0684.00003