Blurred complex exponentiation

Kirby, Jonathan ORCID: https://orcid.org/0000-0003-4031-9107 (2019) Blurred complex exponentiation. Selecta Mathematica-New Series, 25 (5). ISSN 1022-1824

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Abstract

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 the field 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.

Item Type:	Article
Uncontrolled Keywords:	ax-schanuel,complex exponentiation,quasiminimal,zilber conjecture,mathematics(all),physics and astronomy(all) ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	23 Jan 2020 02:49
Last Modified:	13 Dec 2024 01:25
URI:	https://ueaeprints.uea.ac.uk/id/eprint/73748
DOI:	10.1007/s00029-019-0517-4

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