Differential Existential Closedness for the $j$-function

Differential Existential Closedness for the $j$-function

Proc. Amer. Math. Soc. 149 (2021), 1417-1429 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....

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Hauptverfasser: Aslanyan, Vahagn, Eterović, Sebastian, Kirby, Jonathan
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Mathematics - Algebraic Geometry
Mathematics - Logic
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description Proc. Amer. Math. Soc. 149 (2021), 1417-1429 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.
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Soc. 149 (2021), 1417-1429 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. 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Amer. Math. Soc. 149 (2021), 1417-1429 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.</abstract><doi>10.48550/arxiv.2003.10996</doi><oa>free_for_read</oa></addata></record>
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title Differential Existential Closedness for the $j$-function
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