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Differential Existential Closedness for the j-function

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Differential Existential Closedness for the j-function. / Aslanyan, Vahagn; Eterović, Sebastian; Kirby, Jonathan.

In: Proceedings of the American Mathematical Society, 04.09.2020.

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@article{1344aba23b934db3b5a8f23d49321850,
title = "Differential Existential Closedness for the j-function",
abstract = "We prove the Existential Closedness conjecture for the differential equation of the j-function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the j-function have solutions. Its consequences include a complete axiomatisation of j-reducts of differentially closed fields, a dichotomy result for strongly minimal sets in those reducts, and a functional analogue of the Modular Zilber-Pink with Derivatives conjecture.",
keywords = "Ax-Schanuel, j-function, Existential Closedness",
author = "Vahagn Aslanyan and Sebastian Eterovi{\'c} and Jonathan Kirby",
year = "2020",
month = sep,
day = "4",
language = "English",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",

}

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TY - JOUR

T1 - Differential Existential Closedness for the j-function

AU - Aslanyan, Vahagn

AU - Eterović, Sebastian

AU - Kirby, Jonathan

PY - 2020/9/4

Y1 - 2020/9/4

N2 - We prove the Existential Closedness conjecture for the differential equation of the j-function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the j-function have solutions. Its consequences include a complete axiomatisation of j-reducts of differentially closed fields, a dichotomy result for strongly minimal sets in those reducts, and a functional analogue of the Modular Zilber-Pink with Derivatives conjecture.

AB - We prove the Existential Closedness conjecture for the differential equation of the j-function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the j-function have solutions. Its consequences include a complete axiomatisation of j-reducts of differentially closed fields, a dichotomy result for strongly minimal sets in those reducts, and a functional analogue of the Modular Zilber-Pink with Derivatives conjecture.

KW - Ax-Schanuel

KW - j-function

KW - Existential Closedness

M3 - Article

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -

ID: 184237532