A closure operator respecting the modular $j$-function
Logic
2022-10-06 v4
Abstract
We prove some unconditional cases of the Existential Closedness problem for the modular -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 -function and its derivatives, one can define a natural closure operator in three equivalent different ways.
Keywords
Cite
@article{arxiv.2010.00102,
title = {A closure operator respecting the modular $j$-function},
author = {Vahagn Aslanyan and Sebastian Eterović and Jonathan Kirby},
journal= {arXiv preprint arXiv:2010.00102},
year = {2022}
}
Comments
28 pages. Minor corrections