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Demazure, lectures on p-divisible groups, IV.1, isogenies

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Unless otherwise stated let kk be a perfect field of prime characteristic.

We denote write B(K):=Quot(W(k))B(K):=Quot(W(k)) for the quotient field of the Witt ring W(k)W(k). We extend the Frobenius morphism xx (p)x\mapsto x^{(p)} to an automorphism of B(k)B(k). The set of fixed points of xx (p)x\mapsto x^{(p)} in W(k)W(k) is W(F p)= pW(F_p)=\mathbb{Z}_p. The set of fixed points of xx (p)x\mapsto x^{(p)} in B(k)B(k) is B(F p)= pB(F_p)=\mathbb{Q}_p.

Created on May 28, 2012 00:33:54 by Stephan Alexander Spahn (79.227.178.105)