Displaying similar documents to “On elementary equivalence, isomorphism and isogeny”

Siegel’s theorem and the Shafarevich conjecture

Aaron Levin (2012)

Journal de Théorie des Nombres de Bordeaux

Similarity:

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...

The rank of hyperelliptic Jacobians in families of quadratic twists

Sebastian Petersen (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

The variation of the rank of elliptic curves over ℚ in families of quadratic twists has been extensively studied by Gouvêa, Mazur, Stewart, Top, Rubin and Silverberg. It is known, for example, that any elliptic curve over ℚ admits infinitely many quadratic twists of rank ≥ 1 . Most elliptic curves have even infinitely many twists of rank ≥ 2 and examples of elliptic curves with infinitely many twists of rank ≥ 4 are known. There are also certain density results. This paper studies the variation...

Field of moduli versus field of definition for cyclic covers of the projective line

Aristides Kontogeorgis (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli ℝ that can not be defined over ℝ is also given.