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arXiv · 2010.00102

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.

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Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby. 2020-09-30. A closure operator respecting the modular $j$-function. https://doi.org/10.1007/s11856-022-2362-y

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