Fontaine–Mazur conjecture
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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. https://books.google.com/books?id=nqfvCAAAQBAJ&pg=PA180.
- ↑ Calegari, Frank (2011). "Even Galois representations and the Fontaine–Mazur conjecture". Inventiones Mathematicae 185 (1): 1–16. doi:10.1007/s00222-010-0297-0. Bibcode: 2011InMat.185....1C. http://www.math.uchicago.edu/~fcale/papers/EvenPotential.pdf. arXiv preprint
- Fontaine, Jean-Marc; Mazur, Barry (1995), "Geometric Galois representations", in Coates, John; Yau., S.-T., Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), Series in Number Theory, 1, Int. Press, Cambridge, MA, pp. 41–78, ISBN 978-1-57146-026-4
- 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). doi:10.1515/crll.2004.2004.577.147. Bibcode: 2003math......4433D.
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