### A non-abelian algebraic criterion for good reduction of curves

Heilbronn Number Theory Seminar

20th November 2019, 4:00 pm – 5:00 pm

Fry Building, 2.04

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.

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