Journal of the Ramanujan Mathematical Society

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On the Homology of Iwasawa Cohomology Groups


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1 Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario M5S 2E4, Canada
     

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A fundamental observation of Iwasawa gives a criterion for a ℤp⟦Γ⟧-module to be torsion. In this paper, we study and prove a certain extension of this criterion which will be applied to investigate the structure of the homology of the “Iwasawa cohomology groups” of a Galois module over a p-adic Lie extension. Namely, we will answer partially a question of Hachimori on the structure of the homology of the first Iwasawa cohomology groups as modules over Iwasawa algebras and study the pseudo-nullity of the homology of the second Iwasawa cohomology groups and dual fine Selmer groups.
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  • On the Homology of Iwasawa Cohomology Groups

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Authors

Meng Fai Lim
Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario M5S 2E4, Canada

Abstract


A fundamental observation of Iwasawa gives a criterion for a ℤp⟦Γ⟧-module to be torsion. In this paper, we study and prove a certain extension of this criterion which will be applied to investigate the structure of the homology of the “Iwasawa cohomology groups” of a Galois module over a p-adic Lie extension. Namely, we will answer partially a question of Hachimori on the structure of the homology of the first Iwasawa cohomology groups as modules over Iwasawa algebras and study the pseudo-nullity of the homology of the second Iwasawa cohomology groups and dual fine Selmer groups.