Group cohomology of the universal ordinary distribution, by Yi Ouyang

For any odd squarefree integer $r$, we get complete description of the $G_r=\Gal(\mathbb Q(\mu_r)/\math bb Q)$ group cohomology of the universal ordinary distribution $U_r$ in this paper. Moreover, if M is a fixed integer which divides $\ell-1$ for all prime factors $\ell$ of $r$, we study the cohomology group $H^{\ast}(G_r, U_r/MU_r)$. In particular, we explain the mysterious construction of the elements $\kappa_{r'}$ for $r'|r$ in Rubin's appendix to Lang's Cyclotomic fields book, which come exactly from a certain $\mathbb Z/M\mathbb Z$-basis of the cohomology group $H^{0}(G_r, U_r/MU_r)$ through an evaluation map.

Yi Ouyang <youyang@math.umn.edu>