Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, Japan
Abstract:
We have a ring homomorphism Θ from the cohomology of the extended Morava stabilizer group Gn with coefficients in Fw±1] to the cohomology of Gn+1 with coefficients in the graded field F((un))u±1]. In this note we study the behavior of Θ on H1. Then it is shown that Θ is injective on H1 for n1 and for all primes p.