Continuous automorphisms of transcendental closed subfields of \(\mathbb {C}_p\). (English) Zbl 1362.11100
Let \(\mathbb{Q}_p\) be the field of \(p\)-adic numbers and \(\mathbb{C}_p\) be the completion of the algebraic closure of \(\mathbb{Q}_p\) with respect to the \(p\)-adic valuation. In this paper the authors study the problem of continuous automorphisms of transcendental closed subfields of \(\mathbb{C}_p\), which are defined by polynomials. They also consider convergent power series \(G\) with \(p\)-bounded coefficients and show that if such a \(G\) defines a continuous automorphism, then \(G\) must be a polynomial of degree \(1\).
Reviewer: Sudesh Kaur Khanduja (Mohali)
MSC:
| 11S99 | Algebraic number theory: local fields |
References:
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