Naslov
Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields

Autori
Najman, Filip ; Turcas, George C.

Izvornik
International Journal of Number Theory (1793-0421) 17 (2021), 8; 1729-1738

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Galois representations ; elliptic curves ; Fermat equation

Sažetak
In this paper we prove that for every integer d≥1, there exists an explicit constant Bd such that the following holds. Let K be a number field of degree d, let q>max{; ; d−1, 5}; ; be any rational prime that is totally inert in K and E any elliptic curve defined over K such that E has potentially multiplicative reduction at the prime q above q. Then for every rational prime p>Bd, E has an irreducible mod p Galois representation. This result has Diophantine applications within the “modular method”. We present one such application in the form of an Asymptotic version of Fermat’s Last Theorem that has not been covered in the existing literature.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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