Finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental groups. (English) Zbl 1100.14021
It is shown that there are only finitely many isomorphism classes of smooth, hyperbolic curves over the algebraic closure of the finite field \({\mathbb F}_p\), with \(p\) prime, whose fundamental group is isomorphic to a prescribed profinite group. Infinitesimal deformations of generalized Prym varieties are used.
Reviewer: J. W. P. Hirschfeld (Falmer)
MSC:
| 14H25 | Arithmetic ground fields for curves |
| 14G15 | Finite ground fields in algebraic geometry |
| 14H40 | Jacobians, Prym varieties |
| 14G32 | Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) |
| 14H30 | Coverings of curves, fundamental group |
Citations:
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