Displaying similar documents to “On the maximal unramified pro-2-extension over the cyclotomic ℤ 2 -extension of an imaginary quadratic field”

On wild ramification in quaternion extensions

G. Griffith Elder, Jeffrey J. Hooper (2007)

Journal de Théorie des Nombres de Bordeaux

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This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain - 1 (along with some partial results for the more general case). This catalog depends upon the , which as defined in [] is associated with the biquadratic subfield. Moreover we find that quaternion counter-examples to the conclusion of the Hasse-Arf Theorem are extremely rare and can occur only...

On D 5 -polynomials with integer coefficients

Yasuhiro Kishi (2009)

Annales mathématiques Blaise Pascal

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We give a family of D 5 -polynomials with integer coefficients whose splitting fields over ℚ are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.

Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields

Marcin Mazur, Stephen V. Ullom (2008)

Journal de Théorie des Nombres de Bordeaux

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We investigate as Galois module the unit group of biquadratic extensions L / M of number fields. The 2 -rank of the first cohomology group of units of L / M is computed for general M . For M imaginary quadratic we determine a large portion of the cases (including all unramified L / M ) where the index [ V : V 1 V 2 V 3 ] takes its maximum value 8 , where V are units mod torsion of L and V i are units mod torsion of one of the 3 quadratic subfields of L / M .