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  • [hal-00637093] Some remarks concerning the rank of mapping tori and ascending HNN-extensions of abelian groups.

    27 octobre, par Francesco Amoroso, Umberto Zannier
    Let A be a matrix in GL_d(Z) of infinite order. In a recent paper, G. Levitt and V. Metaftsis prove that for any sufficiently large n the matrix A^n is not conjugated to a companion matrix. We first prove a local version of this theorem. Then, we give an effective statement, using linear form (...)
  • [hal-01625058] On the Torsion Anomalous Conjecture in CM abelian varieties

    27 octobre, par Sara Checcoli, Evelina Viada
    The Torsion Anomalous Conjecture (TAC) states that a subvariety V of an abelian variety A has only finitely many maximal torsion anomalous subvarieties. In this work we prove, with an effective method, some cases of the TAC when the ambient variety A has CM, generalising our previous results in (...)
  • [tel-01624238] Contributions to the Langlands program

    26 octobre, par Ildar Gaisin
    This thesis deals with two problems within the Langlands program. For the first problem, in the situation of $\GL_2$ and a non-minuscule cocharacter, we provide a counter-example (under some natural assumptions) to the Rapoport-Zink conjecture, communicated to us by Laurent Fargues.The second (...)
  • [hal-00632997] Computation of the Euclidean minimum of algebraic number fields

    26 octobre, par Pierre Lezowski
    We present an algorithm to compute the Euclidean minimum of an algebraic number field, which is a generalization of the algorithm restricted to the totally real case described by Cerri. With a practical implementation, we obtain unknown values of the Euclidean minima of algebraic number fields (...)
  • [tel-00765252] Questions d’Euclidianité

    26 octobre, par Pierre Lezowski
    Nous étudions l'euclidianité des corps de nombres pour la norme et quelques unes de ses généralisations. Nous donnons en particulier un algorithme qui calcule le minimum euclidien d'un corps de nombres de signature quelconque. Cela nous permet de prouver que de nombreux corps sont euclidiens ou non (...)

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