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 , such that (i) lies in the hyperelliptic locus and (ii) is generated by an abelian differential with two zeros of order . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.
Laurent Ducrohet (2009)
Annales de l’institut Fourier
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Let be a general proper and smooth curve of genus (resp. of genus ) defined over an algebraically closed field of characteristic . When , the action of Frobenius on rank semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order line bundle over . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp....
Greg W. Anderson (2007)
Annales de l’institut Fourier
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For each global field of positive characteristic we exhibit many examples of two-variable algebraic functions possessing properties consistent with a conjectural refinement of the Stark conjecture in the function field case recently proposed by the author. All the examples are Coleman units. We obtain our results by studying rank one shtukas in which both zero and pole are generic, i. e., shtukas not associated to any Drinfeld module.
Gerd Dethloff, Steven S.-Y. Lu (2007)
Annales de l’institut Fourier
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In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate.
In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2:
Jordi Guàrdia (2007)
Annales de l’institut Fourier
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We propose a solution to the hyperelliptic Schottky problem, based on the use of Jacobian Nullwerte and symmetric models for hyperelliptic curves. Both ingredients are interesting on its own, since the first provide period matrices which can be geometrically described, and the second have remarkable arithmetic properties.