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On heights of -adic dynamical systems
Author(s):
Hua-Chieh
Li
Journal:
Proc. Amer. Math. Soc.
130
(2002),
379-386.
MSC (2000):
Primary 11S99;
Secondary 11S31, 14S05
Posted:
July 25, 2001
MathSciNet review:
1862116
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Abstract:
When we consider the properties of the iterates of a noninvertible endomorphism of a formal group, all the roots of iterates of the endomorphism are simple and the full commuting family contains both invertible and noninvertible series. Experimental evidence seems to suggest that for an invertible series to commute with a noninvertible series with only simple roots of iterates, two such commuting power series must be endomorphisms of a single formal group. Lubin proposed four conjectures to support this conjecture. In this paper, we provide answers to these four conjectures.
References:
- 1.
- K. Keating, Automorphisms and Extensions of
, J. Number Theory 41 (1992), no.3, pp. 314-321. MR 93d:13015 - 2.
- H-C. Li,
-adic Periodic Points and Sen's Theorem, J. Number Theory, 56 (1996), no.2, pp. 309-318. MR 96m:11102 - 3.
- H-C. Li, Counting Periodic Points of
-adic Power Series, Compositio Math., 100 (1996), pp. 351-364. MR 97c:11109 - 4.
- H-C. Li,
-adic Dynamical Systems and Formal Groups, Compositio Math., 104 (1996), pp. 41-54. MR 98a:11163 - 5.
- H-C. Li,
-adic Power Series which Commute under Composition, Trans. Amer. Math. Soc., 349 (1997), pp. 1437-1446. MR 97h:11147 - 6.
- J. Lubin & J. Tate, Formal Complex Multiplication in Local Field, Ann. of Math. (2) 81 (1965), pp. 380-387. MR 30:3094
- 7.
- J. Lubin, Nonarchimedean Dynamical Systems, Compositio Math. 94 (1994), pp. 321-346. MR 96g:11140
- 8.
- J. Lubin, personal communication.
- 9.
- S. Sen, On Automorphisms of Local Fields, Ann. of Math. (2) 90 (1969), pp. 33-46. MR 39:5531
- 10.
- J.-P. Serre, Sur les groupes de Galois attachés aux groupes
-divisibles, Proceedings of a Conference on Local Fields held at Driebergen, Springer-Verlag, Berlin and New York, 1967. MR 39:4166
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Additional Information:
Hua-Chieh
Li
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsin Chu, Taiwan, Republic of China
Address at time of publication:
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China
Email:
li@math.nthu.edu.tw
DOI:
10.1090/S0002-9939-01-06166-4
PII:
S 0002-9939(01)06166-4
Received by editor(s):
July 18, 2000
Posted:
July 25, 2001
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2001,
American Mathematical Society
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