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In this paper, we generalize the Hurwitz space which is defined by Fried and Völklein by replacing constant Teichmüller level structures with non-constant Teichmüller level structures defined by finite étale group schemes. As an application, we give some examples of projective general symplectic groups over finite fields which occur as quotients of the absolute Galois group of the field of rational numbers Q.

Non-constant Teichmüller level structures and an application to the Inverse Galois Problem