Resumen de Blurred complex exponentiation

Jonathan Kirby

• It is shown that the complex field equipped with the approximate exponential map, defined up to ambiguity from a small group, is quasiminimal: every automorphism-invariant subset of C is countable or co-countable. If the ambiguity is taken to be from a subfield analogous to a field of constants then the resulting blurred exponential field is isomorphic to the result of an equivalent blurring of Zilber’s exponential field, and to a suitable reduct of a differentially closed field. These results are progress towards Zilber’s conjecture that the complex exponential field itself is quasiminimal. A key ingredient in the proofs is to prove the analogue of the exponential-algebraic closedness property using the density of the group governing the ambiguity with respect to the complex topology.