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@article{JTNB_2015__27_1_67_0, author = {Nuno Freitas and Samir Siksek}, title = {Criteria for {Irreducibility} of mod $p$ {Representations} of {Frey} {Curves}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {67--76}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {27}, number = {1}, year = {2015}, doi = {10.5802/jtnb.894}, mrnumber = {3346965}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.894/} }
TY - JOUR AU - Nuno Freitas AU - Samir Siksek TI - Criteria for Irreducibility of mod $p$ Representations of Frey Curves JO - Journal de théorie des nombres de Bordeaux PY - 2015 SP - 67 EP - 76 VL - 27 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.894/ DO - 10.5802/jtnb.894 LA - en ID - JTNB_2015__27_1_67_0 ER -
%0 Journal Article %A Nuno Freitas %A Samir Siksek %T Criteria for Irreducibility of mod $p$ Representations of Frey Curves %J Journal de théorie des nombres de Bordeaux %D 2015 %P 67-76 %V 27 %N 1 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.894/ %R 10.5802/jtnb.894 %G en %F JTNB_2015__27_1_67_0
Nuno Freitas; Samir Siksek. Criteria for Irreducibility of mod $p$ Representations of Frey Curves. Journal de théorie des nombres de Bordeaux, Tome 27 (2015) no. 1, pp. 67-76. doi : 10.5802/jtnb.894. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.894/
[1] M.A. Bennett, I. Chen, S.R. Dahmen and S. Yazdani, Generalized Fermat equations: a miscellany, preprint, (2013). | MR
[2] M.A. Bennett, S.R. Dahmen, M. Mignotte and S. Siksek, Shifted powers in binary recurrence sequences, Mathematical Proceedings Cambridge Philosophical Society, 158, (2015), 305–329. | MR
[3] C. Breuil, B. Conrad, F. Diamond, R. Taylor, On the modularity of elliptic curves over
[4] H. Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM 240, Springer-Verlag, (2007). | MR | Zbl
[5] A. David, Caractère d’isogénie et critéres d’irréductibilité, arXiv:1103.3892v2.
[6] L. Dieulefait and N. Freitas, Fermat-type equations of signature
[7] N. Freitas, Recipes to Fermat-type equations of the form
[8] N. Freitas and S. Siksek, The asymptotic Fermat’s last theorem for five-sixths of real quadratic fields, Compositio Mathematica, to appear.
[9] N. Freitas, B.V. Le Hung and S. Siksek, Elliptic curves over real quadratic fields are modular, Inventiones Mathematicae, to appear.
[10] K. Fujiwara, Level optimisation in the totally real case, arXiv:math/0602586v1.
[11] F. Jarvis, Level lowering for modular mod
[12] F. Jarvis, Correspondences on Shimura curves and Mazur’s principle at
[13] A. Kraus, Courbes elliptiques semi-stables et corps quadratiques, Journal of Number Theory 60, (1996), 245–253. | MR | Zbl
[14] A. Kraus, Courbes elliptiques semi-stables sur les corps de nombres, International Journal of Number Theory 3, (2007), 611–633. | MR | Zbl
[15] B. Mazur, Rational isogenies of prime degree, Inventiones Math. 44, (1978), 129–162. | MR | Zbl
[16] L. Merel, Bornes pour la torsion des courbes elliptiques sur les corps de nombres, Invent.Math. 124, (1996), 437–449. | MR | Zbl
[17] F. Momose, Isogenies of prime degree over number fields, Compositio Mathematica, 97, (1995), 329–348. | Numdam | MR | Zbl
[18] A. Rajaei, On the levels of mod
[19] K.A. Ribet, On modular representations of
[20] J.-P. Serre, Properiétés galoisiennes des points d’ordre fini des courbes elliptiques, Inventiones Math., 15, (1972), 259–331. | MR | Zbl
[21] S. Siksek, The modular approach to Diophantine equations, chapter 15 of [4].
[22] R. Taylor and A. Wiles, Ring-theoretic properties of certain Hecke algebras, Annals of Mathematics 141, 3 (1995), 553–572. | MR | Zbl
[23] A. Wiles, Modular elliptic curves and Fermat’s Last Theorem, Annals of Mathematics 141, 3 (1995), 443–551. | MR | Zbl
- Generalized Fermat equation: A survey of solved cases, Expositiones Mathematicae, Volume 43 (2025) no. 4, p. 125688 | DOI:10.1016/j.exmath.2025.125688
- Asymptotic solutions of the generalized Fermat-type equation of signature
,3) over totally real number fields, Journal of Number Theory, Volume 274 (2025), pp. 56-71 | DOI:10.1016/j.jnt.2025.01.020 | Zbl:8011962 - On Darmon's program for the generalized Fermat equation. II., Mathematics of Computation, Volume 94 (2025) no. 354, pp. 1977-2003 | DOI:10.1090/mcom/4012 | Zbl:8023301
- On the solutions of
, over totally real fields, Acta Arithmetica, Volume 212 (2024) no. 1, pp. 31-47 | DOI:10.4064/aa221125-23-8 | Zbl:1542.11039 - Perfect powers in elliptic divisibility sequences, Bulletin of the London Mathematical Society, Volume 56 (2024) no. 11, pp. 3331-3345 | DOI:10.1112/blms.13135 | Zbl:7953413
- The Ramanujan Journal, 65 (2024) no. 1, pp. 27-43 | DOI:10.1007/s11139-024-00881-y | Zbl:7920317
- On elliptic curves with
-isogenies over quadratic fields, Canadian Journal of Mathematics, Volume 75 (2023) no. 3, pp. 945-964 | DOI:10.4153/s0008414x22000244 | Zbl:1536.11081 - Explicit Isogenies of Prime Degree Over Quadratic Fields, International Mathematics Research Notices, Volume 2023 (2023) no. 14, p. 11829 | DOI:10.1093/imrn/rnac134
- On the finiteness of perfect powers in elliptic divisibility sequences, Journal de Théorie des Nombres de Bordeaux, Volume 35 (2023) no. 1, pp. 247-258 | DOI:10.5802/jtnb.1244 | Zbl:1525.11026
-
-curves, Hecke characters, and some Diophantine equations. II, Publicacions Matemàtiques, Volume 67 (2023) no. 2, pp. 569-599 | DOI:10.5565/publmat6722304 | Zbl:1527.11027 - Asymptotic Fermat for signatures
using the modular approach, Research in Number Theory, Volume 9 (2023) no. 4, p. 17 (Id/No 71) | DOI:10.1007/s40993-023-00474-6 | Zbl:1531.11033 - Fermat's last theorem and modular curves over real quadratic fields, Acta Arithmetica, Volume 203 (2022) no. 4, pp. 319-351 | DOI:10.4064/aa210812-2-4 | Zbl:1503.11071
- Mathematika, 68 (2022) no. 2, pp. 344-361 | DOI:10.1112/mtk.12127 | Zbl:1539.11059
- Asymptotic Fermat for signatures
and over totally real fields, Mathematika, Volume 68 (2022) no. 4, pp. 1233-1257 | DOI:10.1112/mtk.12162 | Zbl:1534.11041 - Irreducibility of
Galois representations of elliptic curves with multiplicative reduction over number fields, International Journal of Number Theory, Volume 17 (2021) no. 8, pp. 1729-1738 | DOI:10.1142/s1793042121500585 | Zbl:1477.11109 - Shifted powers in Lucas-Lehmer sequences, Research in Number Theory, Volume 5 (2019) no. 1, p. 27 (Id/No 15) | DOI:10.1007/s40993-019-0153-2 | Zbl:1435.11067
- A multi-Frey approach to Fermat equations of signature
, Transactions of the American Mathematical Society, Volume 371 (2019) no. 12, pp. 8651-8677 | DOI:10.1090/tran/7477 | Zbl:1446.11052 - Proceedings of the American Mathematical Society, 145 (2017) no. 10, pp. 4111-4117 | DOI:10.1090/proc/13475 | Zbl:1421.11026
- On the generalized Fermat equation over totally real fields, Acta Arithmetica, Volume 173 (2016) no. 3, pp. 225-237 | DOI:10.4064/aa8171-1-2016 | Zbl:1402.11050
- Modular elliptic curves over real abelian fields and the generalized Fermat equation x2ℓ+ y2m= zp, Algebra Number Theory, Volume 10 (2016) no. 6, p. 1147 | DOI:10.2140/ant.2016.10.1147
- The generalized Fermat equation, Open problems in mathematics, Cham: Springer, 2016, pp. 173-205 | DOI:10.1007/978-3-319-32162-2_3 | Zbl:1440.11037
- Shifted powers in binary recurrence sequences, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 158 (2015) no. 2, pp. 305-329 | DOI:10.1017/s0305004114000681 | Zbl:1371.11081
- Recipes to Fermat-type equations of the form
, Mathematische Zeitschrift, Volume 279 (2015) no. 3-4, pp. 605-639 | DOI:10.1007/s00209-014-1384-5 | Zbl:1369.11027 - On Serre's uniformity conjecture for semistable elliptic curves over totally real fields, Mathematische Zeitschrift, Volume 281 (2015) no. 1-2, pp. 193-199 | DOI:10.1007/s00209-015-1478-8 | Zbl:1376.11046
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