Fontaine–Mazur conjecture

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. Some cases of this conjecture in dimension 2 were already proved by Dieulefait (2004).

References

• 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, MR 1363495 
• Dieulefait, Luis Victor (2004), "Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture" (PDF), J. Reine Angew. Math., 577: 147–151 

External links

• Robert Coleman's lectures on the Fontaine–Mazur conjecture