Leírás
We study towers of local field extensions arising from arithmetic iteration and from higher-dimensional formal groups.
In the one-dimensional setting, iterated extensions have been studied by B. Cais, C. Davis, J. Lubin, and L. Berger, revealing strong links with $p$-adic dynamics; in particular, certain such towers are strictly arithmetically profinite. We consider a more general class of iterated extensions and show that, under natural hypotheses, the resulting towers are in fact deeply ramified. We also construct counterexamples showing that standard valuation-theoretic criteria are insufficient.
We then turn to a higher-dimensional analogue via 2-dimensional Lubin–Tate formal groups. We prove that this class admits a classification in terms of a vector-height invariant and an explicit description of the fields generated by torsion points. In particular, the resulting tower recovers, up to finite index, the maximal totally ramified abelian extension of a suitable base field.
This highlights a sharp contrast between the one-dimensional and higher-dimensional settings and links arithmetic dynamics with higher-dimensional local class field theory.