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p-extensions with restricted ramification - the mixed case

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p-extensions with restricted ramification - the mixed case

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... In general, r K,S is non-obvious and varies from 0 to r 2 + 1 (see Wingberg [6,7], Yamagishi [8], Maire [9,10,11], Labute [12], [13], Vogel [14] for some results and cases where G K,S may be free with less than r 2 + 1 generators and our forthcoming numerical results showing that many Z p -ranks can occur). ...
... Of course, dim F p (H 2 (G K,S , Z/pZ)), giving the minimal number of relations, is easily obtained only when P ⊆ S (equal to rk p (T K,S ) under Leopoldt's conjecture), which shall explain the forthcoming studies about this: [5], [6,7], [8], [11], [12], [14], [36], [44], Haberland [45], [46], El Habibi-Ziane [47] . . .. ...
... where: [11], [14] for some applications). ...
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Part I Algebraic Theory: Cohomology of Profinite Groups.- Some Homological Algebra.- Duality Properties of Profinite Groups.- Free Products of Profinite Groups.- Iwasawa Modules.- Part II Arithmetic Theory: Galois Cohomology.- Cohomology of Local Fields.- Cohomology of Global Fields.- The Absolute Galois Group of a Global Field.- Restricted Ramification.- Iwasawa Theory of Number Fields.- Anabelian Geometry.- Literature.- Index.
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Circular sets of primes of imaginary quadratic number fields Preprints der Forschergruppe Algebraische Zykel und L-Funktionen Regensburg/Leipzig Nr Galois groups of number fields generated by torsion points of elliptic curves
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Vogel, D.: Circular sets of primes of imaginary quadratic number fields. Preprints der Forschergruppe Algebraische Zykel und L-Funktionen Regensburg/Leipzig Nr. 5, 2006 [W] Wingberg, K.: Galois groups of number fields generated by torsion points of elliptic curves. Nagoya Math. J. 104 (1986), 43-53