PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Fermat’s Last Theorem and modular curves over real quadratic fields

Volume 203 / 2022

Philippe Michaud-Jacobs Acta Arithmetica 203 (2022), 319-351 MSC: Primary 11D41; Secondary 11F80, 11G18, 11G05, 14G05. DOI: 10.4064/aa210812-2-4 Published online: 9 May 2022


We study the Fermat equation $x^n+y^n=z^n$ over quadratic fields $\mathbb Q (\sqrt {d})$ for squarefree $d$ with $26 \leq d \leq 97$. By studying quadratic points on the modular curves $X_0(N)$, $d$-regular primes, and working with Hecke operators on spaces of Hilbert newforms, we extend work of Freitas and Siksek to show that for most squarefree $d$ in this range there are no non-trivial solutions to this equation for $n \geq 4$.


  • Philippe Michaud-JacobsMathematics Institute
    University of Warwick
    Coventry, United Kingdom

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image