Group cohomology of the universal ordinary distribution

Abstract

For any odd squarefree integer r, we obtain a complete description of the Gra GalQOm r U=Q group cohomology of the universal ordinary distribution Ur in this paper. Moreover, for M a fixed integer dividing lˇ 1 for all prime factors l of r, we study the cohomology group HOGr; Ur=MUrU. In particular, we explain the construction of the elements kr0 for r 0 jr in Rubin (9), which come exactly from a certain Z=MZ-basis of the cohomology group H 0 OGr; Ur=MUrU through an evaluation map.