Galois-theoretic Characterization of Geometric Isomorphism Classes of Quasi-monodromically Full Hyperbolic Curves with Small Numerical Invariants

Abstract

Let l be a prime number. In the present paper, we prove that the geometric isomorphism class of a quasi-l-monodromically full hyperbolic curve with small numerical invariants over a sub-l-adic field is completely determined by the commensurability class of the kernel of the associated pro-l outer Galois action.