In mathematics, the Fontaine–Mazur conjectures are some conjectures introduced by Fontaine and Mazur (1995) about when p-adic representations of Galois groups of number fields can be constructed from representations on étale cohomology groups of a varieties.[1][2] Some cases of this conjecture in dimension 2 were already proved by Dieulefait (2004).
References
- ↑ Koch, Helmut (2013). "Fontaine-Mazur Conjecture". Galois theory of p-extensions. Springer Science & Business Media. p. 180. ISBN 9783662049679.
- ↑ Calegari, Frank (2011). "Even Galois representations and the Fontaine–Mazur conjecture" (PDF). Inventiones Mathematicae. 185 (1): 1–16. arXiv:1012.4819. Bibcode:2011InMat.185....1C. doi:10.1007/s00222-010-0297-0. S2CID 8937648. arXiv preprint
- Fontaine, Jean-Marc; Mazur, Barry (1995), "Geometric Galois representations", in Coates, John; Yau., S.-T. (eds.), Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), Series in Number Theory, vol. 1, Int. Press, Cambridge, MA, pp. 41–78, ISBN 978-1-57146-026-4, MR 1363495
- Dieulefait, Luis V. (2004). "Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture". Journal für die reine und angewandte Mathematik (Crelle's Journal). 2004 (577). arXiv:math/0304433. Bibcode:2003math......4433D. doi:10.1515/crll.2004.2004.577.147. S2CID 16949796.
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