Nuno Freitas


I am a Research Scientist at ICMAT (CSIC).

Research Interests:

Arithmetic Geometry and Algebraic Number Theory: elliptic curves, modular forms, Galois representations, Diophantine equations.

Contact Information


Instituto de Ciencias Matemáticas (ICMAT),
C/ Nicolás Cabrera 13-15
28049 Madrid, Spain

Office : 309
Email : (firstname).freitas@icmat.es

Research Papers

Preprints

  1. N. Billerey, I. Chen, L. Dieulefait, N. Freitas: On Darmon's program for the generalized Fermat equation, I on arXiv
  2. L. Dembélé, N. Freitas, J. Voight: On Galois inertial types of elliptic curves over Ql on arXiv

Publications

  1. N. Billerey, I. Chen, L. Dieulefait, N. Freitas: On Darmon's program for the generalized Fermat equation II, Mathematics of Computation (to appear) on arXiv
  2. N. Freitas, F. Najman: Two results on xr + yr = dzp, Proceedings of AMS 152 (2024), no. 2, 591--598. on arXiv
  3. N. Billerey, I. Chen, L. Dembélé, L. Dieulefait, N. Freitas: Some extensions of the modular method and Fermat equations of signature (13,13,n), Publicacions Matemàtiques 67 (2023), no. 2. on arXiv
  4. N. Freitas, A. Kraus: On the symplectic type of isomorphisms of the p-torsion of elliptic curves, Memoirs of AMS 277 (2022), no. 1361. on arXiv
  5. J. Cremona, N. Freitas: Global methods for the symplectic type of congruences between elliptic curves, Revista Matemática Iberoamericana 38 (2022), no. 1, 1--32. on arXiv
  6. N. Freitas, A. Kraus, S. Siksek: Local criteria for the unit equation and the asymptotic Fermat's Last Theorem, Proceedings of the National Academy of Sciences 118 (2021), no. 12. on arXiv
  7. N. Freitas, A. Kraus, S. Siksek: On asymptotic Fermat over the Z2-extension of Q, Annales Mathématiques Blaise Pascal 28 (2021), no. 1, 1–6. on arXiv
  8. N. Freitas, A. Kraus, S. Siksek: On the unit equation over cyclic number fields of prime degree, Algebra & Number Theory 15 (2021), no. 10, 2647--2653. on arXiv
  9. N. Freitas, A. Kraus, S. Siksek: On asymptotic Fermat over Zp-extensions of Q, Algebra & Number Theory 14 (2020), no. 9, 2571--2574. on arXiv
  10. N. Freitas, A. Kraus, S. Siksek: Class field theory, Diophantine analysis and the asymptotic Fermat's Last Theorem, Advances in Mathematics 363 (2020). on arXiv
  11. N. Freitas, B. Naskręcki, M. Stoll: The generalized Fermat equation with exponents 2, 3, n, Compositio Mathematica 156 (2020), no. 1, 77--113. on arXiv
  12. N. Freitas, A. Kraus: On the degree of the p-torsion field of elliptic curves over Ql for l ≠ p, Acta Arithmetica 195 (2020), no. 1, 13--55. on arXiv
  13. N. Billerey, I. Chen, L. Dieulefait, N. Freitas: A multi-Frey approach to Fermat equations of signature (r, r, p), Transactions of AMS 371 (2019), no. 12, 8651--8677. on arXiv
  14. M. A. Bennett, C. Bruni, N. Freitas: Sums of two cubes as twisted perfect powers, revisited, Algebra & Number Theory 12 (2018), no. 4, 959--999. on arXiv
  15. N. Billerey, I. Chen, L. Dieulefait, N. Freitas: A result on the equation xp + yp = zr using Frey abelian varieties, Proceedings of AMS 145 (2017), no. 10, 4111--4117. on arXiv
  16. N. Freitas: On the Fermat-type equation x3 + y3 = zp, Commentarii Mathematici Helvetici 91 (2016), 295--304. on arXiv
  17. N. Freitas, A. Kraus: An application of the symplectic argument to some Fermat-type equations, C. R. Math. Acad. Sci. Paris 354 (2016), no. 8, 751--755. on arXiv
  18. N. Freitas, S. Siksek: The Asymptotic Fermat's Last Theorem for Five-Sixths of Real Quadratic Fields, Compositio Mathematica 151 (2015), no. 8, 1395--1415. on arXiv
  19. N. Freitas, B. Le Hung, S. Siksek: Elliptic Curves over Real Quadratic Fields are Modular, Inventiones Mathematicae 201 (2015), no. 1, 159--206. on arXiv
  20. N. Freitas, S. Siksek: Criteria for irreducibility of mod p representations of Frey curves, Journal de Théorie des Nombres de Bordeaux 27 (2015), 67--76. on arXiv
  21. N. Freitas, S. Siksek: Fermat's Last Theorem over some small real quadratic fields, Algebra & Number Theory 9 (2015), no. 4, 875--895. on arXiv
  22. L. Dieulefait, N. Freitas: Base change for Elliptic Curves over Real Quadratic Fields, C. R. Math. Acad. Sci. Paris 353 (2015), no. 1, 1--4. on arXiv
  23. N. Freitas: Recipes for Fermat-type equations of the form xr + yr = Czp, Mathematische Zeitschrift 279 (2015), no. 3-4, 605--639. on arXiv
  24. N. Freitas, P. Tsaknias: Criteria for p-ordinarity of families of elliptic curves over infinitely many number fields, International Journal of Number Theory 11 (2015), no. 1, 81--87. on arXiv
  25. L. Dieulefait, N. Freitas: The Fermat-type equations x5 + y5 = 2zp or 3zp solved through Q-curves, Mathematics of Computation 83 (2014), no. 286, 917--933. on arXiv
  26. L. Dieulefait, N. Freitas: Fermat-type equations of signature (13, 13, p) via Hilbert cuspforms, Mathematische Annalen 357 (2013), no. 3, 987--1004. on arXiv