Quasiminimality of complex powers

Francesco Gallinaro; Jonathan Kirby

doi:10.1017/fms.2024.82

Quasiminimality of complex powers

Francesco Gallinaro, Jonathan Kirby

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

7 Downloads (Pure)

Abstract

The complex field, equipped with the multivalued functions of raising to each complex power, is quasiminimal, proving a conjecture of Zilber and providing evidence towards his stronger conjecture that the complex exponential field is quasiminimal.

Original language	English
Article number	e123
Journal	Forum of Mathematics, Sigma
Volume	12
DOIs	https://doi.org/10.1017/fms.2024.82
Publication status	Published - 13 Dec 2024

Keywords

math.LO

Access to Document

10.1017/fms.2024.82Licence: CC BY

QM_of_complex_powers_acceptedAccepted author manuscript, 492 KBLicence: CC BY

http://arxiv.org/pdf/2304.06450v2

Exponentially Algebraically closed fields.
Kirby, J.
Engineering and Physical Sciences Research Council
1/09/19 → 31/08/22
Project: Research

Cite this

@article{397fca8d53c24c1cb9831a6432c1dfe0,

title = "Quasiminimality of complex powers",

abstract = "The complex field, equipped with the multivalued functions of raising to each complex power, is quasiminimal, proving a conjecture of Zilber and providing evidence towards his stronger conjecture that the complex exponential field is quasiminimal. ",

keywords = "math.LO",

author = "Francesco Gallinaro and Jonathan Kirby",

note = "Funding information: Both authors were supported by EPSRC grant EP/S017313/1. The first author was partially supported by a London Mathematical Society Early Career Fellowship and by the program GeoMod ANR-19-CE40-0022-01 (ANR-DFG).",

year = "2024",

month = dec,

day = "13",

doi = "10.1017/fms.2024.82",

language = "English",

volume = "12",

journal = "Forum of Mathematics, Sigma",

issn = "2050-5094",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Quasiminimality of complex powers

AU - Gallinaro, Francesco

AU - Kirby, Jonathan

N1 - Funding information: Both authors were supported by EPSRC grant EP/S017313/1. The first author was partially supported by a London Mathematical Society Early Career Fellowship and by the program GeoMod ANR-19-CE40-0022-01 (ANR-DFG).

PY - 2024/12/13

Y1 - 2024/12/13

N2 - The complex field, equipped with the multivalued functions of raising to each complex power, is quasiminimal, proving a conjecture of Zilber and providing evidence towards his stronger conjecture that the complex exponential field is quasiminimal.

AB - The complex field, equipped with the multivalued functions of raising to each complex power, is quasiminimal, proving a conjecture of Zilber and providing evidence towards his stronger conjecture that the complex exponential field is quasiminimal.

KW - math.LO

U2 - 10.1017/fms.2024.82

DO - 10.1017/fms.2024.82

M3 - Article

VL - 12

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

SN - 2050-5094

M1 - e123

ER -

Quasiminimality of complex powers

Abstract

Keywords

Access to Document

Projects

Exponentially Algebraically closed fields.

Cite this