Displaying similar documents to “Intersection-theoretical computations on v e r l i n e M g ”

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...

Finiteness results for Teichmüller curves

Martin Möller (2008)

Annales de l’institut Fourier

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We show that for each genus there are only finitely many algebraically primitive Teichmüller curves C , such that (i) C lies in the hyperelliptic locus and (ii) C is generated by an abelian differential with two zeros of order g - 1 . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.

On the discrete logarithm problem for plane curves

Claus Diem (2012)

Journal de Théorie des Nombres de Bordeaux

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In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem for non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of O ˜ ( q ) , where q is the cardinality of the ground field. Moreover, it is proven that for every fixed natural number d ≥ 4 the following holds: We consider the discrete logarithm problem for curves given...