Displaying similar documents to “Field of moduli versus field of definition for cyclic covers of the projective line”

Constructing class fields over local fields

Sebastian Pauli (2006)

Journal de Théorie des Nombres de Bordeaux

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Let K be a 𝔭 -adic field. We give an explicit characterization of the abelian extensions of K of degree p by relating the coefficients of the generating polynomials of extensions L / K of degree p to the exponents of generators of the norm group N L / K ( L * ) . This is applied in an algorithm for the construction of class fields of degree p m , which yields an algorithm for the computation of class fields in general.

The field-of-norms functor and the Hilbert symbol for higher local fields

Victor Abrashkin, Ruth Jenni (2012)

Journal de Théorie des Nombres de Bordeaux

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The field-of-norms functor is applied to deduce an explicit formula for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic p > 2 in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov’s explicit formula.

Siegel’s theorem and the Shafarevich conjecture

Aaron Levin (2012)

Journal de Théorie des Nombres de Bordeaux

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It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field k and any finite set of places S of k , one can effectively compute the set of isomorphism classes of hyperelliptic curves over k with good reduction outside S . We show here that an extension of this result to an effective Shafarevich conjecture for of hyperelliptic curves of genus g would imply an effective version of Siegel’s theorem for integral points...