When is a $p$-adic power series an endomorphism of a formal group?
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- by Hua-Chieh Li PDF
- Proc. Amer. Math. Soc. 124 (1996), 2325-2329 Request permission
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
- Neal Koblitz, $p$-adic numbers, $p$-adic analysis, and zeta-functions, Graduate Texts in Mathematics, Vol. 58, Springer-Verlag, New York-Heidelberg, 1977. MR 0466081, DOI 10.1007/978-1-4684-0047-2
- J. Lubin, Nonarchimedean dynamical systems, Compositio Math. 94 (1994), 321–346.
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.
- Email: li@math.nthu.edu.tw
- Received by editor(s): June 25, 1994
- Received by editor(s) in revised form: February 9, 1995
- Communicated by: William W. Adams
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2325-2329
- MSC (1991): Primary 11S99; Secondary 11S31, 14L05
- DOI: https://doi.org/10.1090/S0002-9939-96-03308-4
- MathSciNet review: 1322933