Covers of the multiplicative group of an algebraically closed field of characteristic zero

Details Covers of the multiplicative group of an algebraically closed field of characteristic zero Covers of the multiplicative group of an algebraically closed field of characteristic zero

2004-01-22

arxiv.org/abs/math/0401301v1

Mathematics

Commutative Algebra

25 pages, Latex

Scientific paper

We study the universal cover of the complex one-dimensional torus as a model-theoretic structure in a natural language. We consider also abstract covers of one-dimensional tori over algebraically closed fields of characteristic zero. The main result states that the structures can be described uniquely up to isomorphism by a simple (non-first order) sentence, given a fixed uncountable cardinality of the underlying field. The proof reduces to the Kummer theory of cyclic Galois extensions over some, not necessarily finitely generated fields.

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