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Displaying similar documents to “On the discrete logarithm problem for plane curves”

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...

Linearly Normal Curves in P^n

Pasarescu, Ovidiu (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 14H45, 14H50, 14J26. We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in [4], and extended to P^4 and P^5 in [10]. In both these papers is used the idea appearing in [4] and consisting in adding hyperplane sections to the curves constructed in [6] (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In...

Variations on a theme of Runge: effective determination of integral points on certain varieties

Aaron Levin (2008)

Journal de Théorie des Nombres de Bordeaux

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We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge’s theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge’s theorem due to Bombieri. We then take up the study of how Runge’s method may be expanded by taking advantage of certain coverings. We prove both a result for arbitrary curves and a more explicit result for superelliptic curves. As an application...

Computation of 2-groups of positive classes of exceptional number fields

Jean-François Jaulent, Sebastian Pauli, Michael E. Pohst, Florence Soriano–Gafiuk (2008)

Journal de Théorie des Nombres de Bordeaux

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We present an algorithm for computing the 2-group 𝒞 ℓ F p o s of the positive divisor classes in case the number field F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel W K 2 ( F ) in K 2 ( F ) .