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• W3105462224 startingPage "493" @default.
• W3105462224 abstract "We give a construction of quasiminimal fields equipped with pseudo-analytic maps, generalising Zilber's pseudo-exponential function. In particular we construct pseudo-exponential maps of simple abelian varieties, including pseudo-$wp$-functions for elliptic curves. We show that the complex field with the corresponding analytic function is isomorphic to the pseudo-analytic version if and only the appropriate version of Schanuel's conjecture is true and the corresponding version of the strong exponential-algebraic closedness property holds. Moreover, we relativize the construction to build a model over a fairly arbitrary countable subfield and deduce that the complex exponential field is quasiminimal if it is exponentially-algebraically closed. This property asks only that the graph of exponentiation have non-trivial intersection with certain algebraic varieties but does not require genericity of these points. Furthermore Schanuel's conjecture is not required as a condition for quasiminimality." @default.
• W3105462224 created "2020-11-23" @default.
• W3105462224 creator A5009115527 @default.
• W3105462224 creator A5073358589 @default.
• W3105462224 date "2018-06-12" @default.
• W3105462224 modified "2023-09-25" @default.
• W3105462224 title "Pseudo-exponential maps, variants, and quasiminimality" @default.
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• W3105462224 doi "https://doi.org/10.2140/ant.2018.12.493" @default.
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