  We give a new method for solving a problem originally solved about 20 years
ago by Sinnott and Kubert, namely that of computing the cohomology of the
universal ordinary distribution with respect to the action of the two-element
group generated by complex conjugation. We develop the method in sufficient
generality so as to be able to calculate analogous cohomology groups in the
function field setting which have not previously been calculated. In
particular, we are able to confirm a conjecture of L.~S.~Yin conditional on
which Yin was able to obtain results on unit indices generalizing those of
Sinnott in the classical cyclotomic case and Galovich-Rosen in the Carlitz
cyclotomic case. The Farrell-Tate cohomology theory for groups of finite
virtual cohomological dimension plays a key role in our proof of Yin's
conjecture. The methods developed in the paper have recently been used by
P.~Das to illuminate the structure of the Galois group of the algebraic
extension of the rational number field generated by the roots of unity and the
algebraic $\Gamma$-monomials.
  This paper has appeared as Contemp. Math. 224 (1999) 1-27.
