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On a good reduction criterion for proper polycurves with sections. (English) Zbl 1451.11056
Summary: We give a good reduction criterion for proper polycurves with sections, i.e., successive extensions of family of curves with section, under a mild assumption. This criterion is a higher dimensional version of the good reduction criterion for hyperbolic curves given by T. Oda [J. Number Theory 34, No. 2, 225–228 (1990; Zbl 0716.14014); ibid. 53, No. 2, 342–355 (1995; Zbl 0844.14013)] and A. Tamagawa [Compos. Math. 109, No. 2, 135–194 (1997; Zbl 0899.14007)].
##### MSC:
 11G20 Curves over finite and local fields 11G30 Curves of arbitrary genus or genus $$\ne 1$$ over global fields
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