Mathematics – Number Theory
Scientific paper
1997-10-21
Mathematics
Number Theory
Scientific paper
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.
No associations
LandOfFree
A double complex for computing the sign-cohomology of the universal ordinary distribution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A double complex for computing the sign-cohomology of the universal ordinary distribution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A double complex for computing the sign-cohomology of the universal ordinary distribution will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-80010