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.
Greg W. Anderson <email@example.com>