Differential Existential Closedness for the $j$-function
Logic
2021-06-04 v2 Algebraic Geometry
Abstract
We prove the Existential Closedness conjecture for the differential equation of the -function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the -function have solutions. Its consequences include a complete axiomatisation of -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
Cite
@article{arxiv.2003.10996,
title = {Differential Existential Closedness for the $j$-function},
author = {Vahagn Aslanyan and Sebastian Eterović and Jonathan Kirby},
journal= {arXiv preprint arXiv:2003.10996},
year = {2021}
}
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