A closure operator respecting the modular j-function

Vahagn Aslanyan; Sebastian Eterović; Jonathan Kirby

doi:10.1007/s11856-022-2362-y

A closure operator respecting the modular j-function

Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby

Algebra, Number Theory, Logic, and Representations (ANTLR)

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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 language	English
Pages (from-to)	321–357
Number of pages	37
Journal	Israel Journal of Mathematics
Volume	253
Early online date	5 Oct 2022
DOIs	https://doi.org/10.1007/s11856-022-2362-y
Publication status	Published - Mar 2023

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Extending_j_derivationsAccepted author manuscript, 570 KB

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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.",

author = "Vahagn Aslanyan and Sebastian Eterovi{\'c} and Jonathan Kirby",

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AB - 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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A closure operator respecting the modular j-function

Abstract

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Exponentially Algebraically closed fields.

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A closure operator respecting the modular j-function

Abstract

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Exponentially Algebraically closed fields.

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