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  • [hal-00634643] Examples of norm-Euclidean ideal classes

    25 octobre 2017, par Pierre Lezowski
    In 1978, Lenstra defined the notion of Euclidean ideal class. Using a slight modification of an algorithm computing the Euclidean minimum, we give new examples of number fields with norm-Euclidean ideal classes. Extending the results of Cioffari, we also establish the complete list of pure (...)
  • [hal-01258906] The Euclidean algorithm in quintic and septic cyclic fields

    25 octobre 2017, par Pierre Lezowski, Kevin Mcgown
    Conditionally on the Generalized Riemann Hypothesis (GRH), we prove the following results: (1) a cyclic number field of degree $5$ is norm-Euclidean if and only if $\Delta=11^4,31^4,41^4$; (2) a cyclic number field of degree $7$ is norm-Euclidean if and only if $\Delta=29^6,43^6$; (3) there are (...)
  • [hal-01622008] Unramified 2-extensions of totally imaginary number fields and 2-adic analytic groups

    25 octobre 2017, par Christian Maire
    — Let K be a totally imaginary number field. Denote by G ur K (2) the Galois group of the maximal unramified pro-2 extension of K. By comparing cup-products in étale cohomology of SpecO K and cohomology of uniform pro-2 groups, we obtain situations where G ur K (2) has no non-trivial uniform (...)
  • [hal-01622014] Analytic lie extensions of number fields with cyclic fixed points and tame ramification

    25 octobre 2017, par Farshid Hajir, Christian Maire
    — Let p be a prime number and K an algebraic number field. What is the arithmetic structure of Galois extensions L/K having p-adic analytic Galois group Γ = Gal(L/K)? The celebrated Tame Fontaine-Mazur conjecture predicts that such extensions are either deeply ramified (at some prime dividing p) (...)
  • [hal-01623558] Tchebotarev theorems for function fields

    25 octobre 2017, par Sara Checcoli, Pierre Dèbes
    We prove Tchebotarev type theorems for function field extensions over various base fields: number fields, finite fields, p-adic fields, PAC fields, etc. The Tchebotarev conclusion - existence of appropriate cyclic residue extensions - also compares to the Hilbert specialization property. It is (...)

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