Group cohomology of universal ordinary distribution
Yi Ouyang
Abstract
For any odd squarefree integer r, we get complete description of the Gr=Gal(Q(mur)/Q) group cohomology of the universal ordinary distribution Ur in this paper. Moreover, if M is a fixed integer which divides l-1 for all prime factors l of r, we study the cohomology group H*(Gr, Ur/MUr). In particular, we explain the mysterious construction of the elements kappar' for r'|r in Rubin's construction of Kolyvagin elements, which come exactly from a certain Z/M Z-basis of the cohomology group H0(Gr, Ur/MUr) through an evaluation map.
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