Ramified primes in the field of moduli of branched coverings of curves

DOI10.1016/0021-8693(89)90303-7zbMath0698.14024OpenAlexW1984706147MaRDI QIDQ912164

Sybilla Beckmann

Publication date: 1989

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90303-7

zbMATH Keywords

bad reductionfield of definitionfield of moduli of the coveringgalois branched covering

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Families, moduli of curves (algebraic) (14H10) Algebraic moduli problems, moduli of vector bundles (14D20) Coverings of curves, fundamental group (14H30) Coverings in algebraic geometry (14E20)

Related Items

Reduction of the Hurwitz space of metacyclic covers ⋮ Ramification in the field of moduli. ⋮ On the reduction modulo \(p\) of an absolutely irreducible polynomial \(f(x,y)\) ⋮ Stable reduction of three point covers ⋮ Some coverings defined over \(\mathbb{Q}\) ⋮ Period computations for covers of elliptic curves ⋮ The p-rank of the reduction mod p of Jacobians and Jacobi sums ⋮ Belyi pairs and fried families ⋮ On some notions of good reduction for endomorphisms of the projective line ⋮ Fields of moduli of three-point \(G\)-covers with cyclic \(p\)-Sylow. II ⋮ Potential energy function based on the narcissus constant, its square and its cube ⋮ Ramification in iterated towers for rational functions ⋮ Belyi functions for hyperbolic hypergeometric-to-Heun transformations ⋮ Proof of the existence of certain triples of polynomials ⋮ Arithmetic descent of specializations of Galois covers ⋮ Good reduction of certain covers \(\mathbb{P}^1\to\mathbb{P}^1\) ⋮ Three point covers with bad reduction ⋮ Ramified Primes in the Field of Definition for the Mordell-Weil Group of an Elliptic Surface ⋮ Bounding the degree of Belyi polynomials ⋮ Numerical calculation of three-point branched covers of the projective line ⋮ The Belyi degree of a curve is computable ⋮ Covers of elliptic curves with unique, totally ramified branch points

Cites Work

• Algebraic geometry and analytic geometry
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• Hurwitz schemes and irreducibility of moduli of algebraic curves
• Éléments de géométrie algébrique. III: Étude cohomologique des faisceaux cohérents. (Séconde partie). Rédigé avec la colloboration de J. Dieudonné
• Konstruktion von Zahl- und Funktionenkörpern mit vorgegebener Galoisgruppe.
• Fields of definition of function fields and hurwitz families — groups as galois groups
• Note on coefficient fields of complete local rings
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