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Application de la notion de <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϕ</mml:mi></mml:math>-objet à l’étude du groupe des classes d’idéaux des extensions abéliennes
We revisit, in an elementary way, the classical statement of various "Main Conjectures" for p-class groups H K and p-ramified torsion groups T K of abelian fields K, in the non semisimple case p | [K : Q].The classical "algebraic" definition of the p-adic isotopic components, H alg K,ϕ , …