Spahn display of a formal p-divisible group (Rev #2, changes)

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Let $R\in CRing$ a commutative unitary ring. Let $W(R)$ denote the ring of Witt vectors of $R$ . Let

w_n:\begin{cases} W(R)\to R \\ (x_0,\dots,x_i,\dots)\mapsto x_0^{p^n}+p x_1^{p^{n-1}}+ \dots + p^n x_n \end{cases}

denote the morphism of rings assigning to Witt vector its correspnding Witt polynomial. Let

w_n:\begin{cases} W(R)\to W(R) \\ (x_0,\dots,x_i,\dots)\mapsto (0,x_0,\dots,x_i,\dots) \end{cases}

denote the Verschiebung morphism? which is a morphism of the underlying additive groups. Let $p$ be a prime number? and let

F:W(R)\to W(R)

denote the Frobenius morphism?. Then Frobenius, Verschiebung, and the Witt-polynomial morphism satisfy the ‘’ $p$ -adic Witt-Frobenius identities’’:

w_n(F(x))=w_{n+1}(x)\; n\ge 0

w_n(V(x))=w_{n-1}(x)\; n\gt 0

w_0(V(x))=0

FV=p

VF(xy)=xV(y)

References

T. Zink, the display of a formal p-divisible group, to appear in Asterisque, pdf
T. Zink, Windows for displays of p-divisible groups. in:Moduli of Abelian Varieties, Progress in Mathematics 195, Birkhäuser 2001, pdf

Revision on June 4, 2012 at 13:18:36 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.