Finiteness of Isomorphism Classes of Hyperbolic Polycurves with Prescribed Fundamental Groups

Abstract

<jats:title>Abstract</jats:title><jats:p>In the present paper, we show that there are at most finitely many isomorphism classes of hyperbolic polycurves (i.e., successive extensions of families of hyperbolic curves) over certain types of fields whose étale fundamental group is isomorphic to a prescribed profinite group.</jats:p>

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