  Colmez conjectured a product formula for periods of abelian varieties with
complex multiplication by a field K, analogous to the standard product formula
in algebraic number theory. He proved this conjecture up to a rational power of
2 for K/Q abelian. In this paper, we complete the proof of Colmez for K/Q
abelian by eliminating this power of 2. Our proof relies on analyzing the
Galois action on the De Rham cohomology of Fermat curves in mixed
characteristic (0, 2), which in turn relies on understanding the stable
reduction of Z/2^n-covers of the projective line, branched at three points.
