LUBIN ’ S CONJECTURE FOR FULL p - ADIC DYNAMICAL SYSTEMS by
نویسندگان
چکیده
— We give a short proof of a conjecture of Lubin concerning certain families of p-adic power series that commute under composition. We prove that if the family is full (large enough), there exists a Lubin-Tate formal group such that all the power series in the family are endomorphisms of this group. The proof uses ramification theory and some p-adic Hodge theory.
منابع مشابه
Canonical and filling subgroups of formal groups
Let F be a one-dimensional full or almost full p-adic formal group. We look for finite subgroups C of F for which the quotient formal group F/C is full. In particular, we investigate the connection between such groups and the congruence-torsion subgroups of F described in Lubin, 1979. In doing so, we prove a conjecture of Jonathan Lubin concerning this relationship when F
متن کاملEndomorphism rings of almost full formal groups
Let oK be the integral closure of Zp in a finite field extension K of Qp, and let F be a one-dimensional full formal group defined over oK . We study certain finite subgroups C of F and prove a conjecture of Jonathan Lubin concerning the absolute endomorphism ring of the quotient F/C when F has height 2. We also investigate ways in which this result can be generalized to p-adic formal groups of...
متن کاملalgebraic and arithmetic dynamics bibliographical database
References [1] S. Akiyama, T. Borbéli, H. Brunotte, A. Pethö, and J. Thuswaldner. Generalized radix representations and dynamical systems i. Acta Math. Hungarica., 108:207–238, 2005. [2] S. Akiyama, H. Brunotte, A. Pethö, and J. Thuswaldner. Generalized radix representations and dynamical systems ii. Acta Arith., 121:21–61, 2006. [3] S. Akiyama and N Gjini. On the connectedness of self-affine a...
متن کاملTHE CRYSTALLINE PERIOD OF A HEIGHT ONE p-ADIC DYNAMICAL SYSTEM
Let f be a continuous ring endomorphism of ZpJxK/Zp of degree p. We prove that if f acts on the tangent space at 0 by a uniformizer and commutes with an automorphism of infinite order, then it is necessarily an endomorphism of a formal group over Zp. The proof relies on finding a stable embedding of ZpJxK in Fontaine’s crystalline period ring with the property that f appears in the monoid of en...
متن کاملBehavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups
We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups. We prove Arthur's conjecture, the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group, for quasi-split special unitary groups and their inner forms. Furthermore, we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms. This w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016