A closure operator respecting the modular j-function

Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby

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Abstract

We prove some unconditional cases of the Existential Closedness problem for the modular j-function. For this, we show that for any finitely generated field we can find a “convenient” set of generators. This is done by showing that in any field equipped with functions replicating the algebraic behaviour of the modular j-function and its derivatives, one can define a natural closure operator in three equivalent different ways.
Original languageEnglish
Pages (from-to)321–357
Number of pages37
JournalIsrael Journal of Mathematics
Volume253
Early online date5 Oct 2022
DOIs
Publication statusPublished - Mar 2023

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