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When is a $p$-adic power series
an endomorphism of a formal group?

Author: Hua-Chieh Li
Journal: Proc. Amer. Math. Soc. 124 (1996), 2325-2329
MSC (1991): Primary 11S99; Secondary 11S31, 14L05
MathSciNet review: 1322933
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Abstract: If $f(x)$ is a noninvertible endomorphism of a formal group, then we have that $f(x)$ commutes with an invertible series and $\overline {\mathcal {O}}[[x]]$ is Galois over $\overline {\mathcal {O}}[[f^n(x)]]$ for all $n\in \mathbf {N}$. We shall prove that the converse of this statement is also true.

References [Enhancements On Off] (What's this?)

  • 1. Neal Koblitz, 𝑝-adic numbers, 𝑝-adic analysis, and zeta-functions, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, Vol. 58. MR 0466081
  • 2. J. Lubin, Nonarchimedean dynamical systems, Compositio Math. 94 (1994), 321--346. CMP 95:06

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Additional Information

Hua-Chieh Li
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Address at time of publication: Department of Mathematics, National Tsin Hua University, Hsin Chu, Taiwan, R.O.C.

Received by editor(s): June 25, 1994
Received by editor(s) in revised form: February 9, 1995
Communicated by: William W. Adams
Article copyright: © Copyright 1996 American Mathematical Society