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On the bad reduction of Shimura varieties. (English) Zbl 0716.14010
Automorphic forms, Shimura varieties, and L-functions. Vol. II, Proc. Conf., Ann Arbor/MI (USA) 1988, Perspect. Math. 11, 253-321 (1990).
[For the entire collection see Zbl 0684.00004.]
This paper is a survey article dealing with the reduction behaviour of Shimura varieties at primes of bad reduction. It is a well readable account of the state of affairs. In the first part the author reviews some cases where there is a rather good description of the bad fibre. - In the second part the local factor of the Hasse-Weil zeta function at primes of bad reduction is discussed. The remaining part deals with the case of the so-called “fake” unitary groups where a conjectural formula for the local zeta factor is given.
Reviewer: G.van der Geer

MSC:
14G35 Modular and Shimura varieties
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
11G18 Arithmetic aspects of modular and Shimura varieties