Valentina Di Proietto

A non-abelian algebraic criterion for good reduction of curves

For a family of proper hyperbolic complex curves f : X → Δ* over a punctured disc Δ* with semistable reduction at the center, Oda proved, with transcendental methods, that the outer monodromy action of π_1(Δ*) ≅ Z on the classical unipotent fundamental group of the generic fiber of f is trivial if and only if f has good reduction at the center. In this talk I explain a joint work with B. Chiarellotto and A. Shiho in which we give a purely algebraic proof of Oda’s result.