Group cohomology of universal ordinary distribution

Details Group cohomology of universal ordinary distribution Group cohomology of universal ordinary distribution

1999-11-05

arxiv.org/abs/math/9911032v1

J. reine. angew. Math. 537(2001), 1-32

Mathematics

Number Theory

30 pages, 1 figure, 1 appendix by Prof. Greg Anderson

Scientific paper

For any odd squarefree integer r, we get complete description of the G_r=Gal(Q(mu_r)/Q) group cohomology of the universal ordinary distribution U_r 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^{*}(G_r, U_r/MU_r). In particular, we explain the mysterious construction of the elements kappa_{r'} for r'|r in Rubin's construction of Kolyvagin elements, which come exactly from a certain Z/M Z-basis of the cohomology group H^{0}(G_r, U_r/MU_r) through an evaluation map.

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