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Non-constant Teichmüller level structures and an application to the inverse Galois problem. (English) Zbl 1393.12007

Summary: In this paper, we generalize the Hurwitz space which is defined by M. D. Fried und H. Völklein [Math. Ann. 290, No. 4, 771–800 (1991; Zbl 0763.12004)] 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 \(\mathbb{Q}\).

MSC:

12F12 Inverse Galois theory
11R32 Galois theory
14D23 Stacks and moduli problems

Citations:

Zbl 0763.12004
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