S-unit equations and the asymptotic Fermat conjecture over number fields

Ozman, Ekin; Siksek, Samir

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S-unit equations and the asymptotic Fermat conjecture over number fields

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Ozman, Ekin
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2003.11289
(Preprint)

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Citation

Ozman, E., & Siksek, S. (2022). S-unit equations and the asymptotic Fermat conjecture over number fields. In K. Kurşungöz, & A. Zeytin (Eds.), Number Theory: Proceedings of the Journées Arithmétiques, 2019, XXXI, held at Istanbul University (pp. 83-103). Berlin [u.a.]: De Gruyter.

Cite as: https://hdl.handle.net/21.11116/0000-000A-564A-3

Abstract

Recent attempts at studying the Fermat equation over number fields have
uncovered an unexpected and powerful connection with $S$-unit equations. In
this expository paper we explain this connection and its implications for the
asymptotic Fermat conjecture.