Abstract
Abstract.We prove that for every ordinary genus-2 curve X over a finite field κ of characteristic 2 with Aut(X/κ) = ℤ/2ℤ × S3 there exist SL(2; κ[[s]])-representations of π1(X) such that the image of π1(X̄) is infinite. This result produces a family of examples similar to Y. Laszlo’s counterexample to A. J. de Jong’s question regarding the finiteness of the geometric monodromy of representations of the fundamental group.
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