Fields of constants of integral derivations on a -adic field

Authors:
Henry W. Thwing and Nickolas Heerema

Journal:
Trans. Amer. Math. Soc. **195** (1974), 277-290

MSC:
Primary 12F15

MathSciNet review:
0387259

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Abstract: Let be a *p*-adic subfield of a *p*-adic field *K* with residue fields . If is algebraically closed in *K* and *k* is finitely generated over then is the subfield of constants of an analytic derivation on *K* or equivalently, is the invariant subfield of an inertial automorphism of *K*. If (1) is separably algebraically closed in *k*, (2) , and (3) *k* is not algebraic over then there exists a *p*-adic subfield over which is algebraically closed in *K*. All subfields over are algebraically closed in *K* if and only if is algebraically closed in *k*. Every derivation on *k* trivial on lifts to a derivation on *K* trivial on if *k* is separable over . If *k* is finitely generated over the separability condition is necessary. Applications are made to invariant fields of groups of inertial automorphisms on *p*-adic fields and of their ramification groups.

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0387259-3

Keywords:
Analytic derivation,
integral derivation,
field of constants,
*p*-adic field,
relative algebraic closure

Article copyright:
© Copyright 1974
American Mathematical Society