16

JURGEN RITTER AND ALFRED WEISS

Thus, in K0T(ZiG),

[coker (pc) = [coker (pj\ + [coker $]

and so

THEOREM A. Let K be a totally real field satisfying LeopoldVs conjecture. Then ify' =

Indeed, Q^ , Sl^c , Q$ differ from the respective cokernels of (p\, (pc ? 4 by

29[|Gf|,X]

with

X = Zt 0 L, Z/ 0 A* , A/G respectively. The short exact sequence Z/ ® L - Z/ g A* -» A/G

implies the cancellation of these 9-terms.

Note that Q^z is the Qp in the Lifted Root Number Conjecture at /, with (f : AS —» • E the

restriction of ZS — fl s

^pX

• Therefore, Theorem A is proved.