Some cases of the Fontaine-Mazur conjecture
Let \(p\) be a prime, \(K\) an algebraic number field and \(L\) the maximal unramified \(p\)-extension of \(K\). Fontaine and Mazur have conjectured that there does not exist a \(p\)-adic representation of \(\text{Gal}(L/K)\) with infinite image. The author proves that the conjecture is true if \(K\) is a normal extension of prime degree \(l \neq p\) of a field \(F\) such that the class number of \(F\) is prime to \(p\).
nonexistence of an infinite everywhere unramified Galois pro-\(p\)-extension
\(p\)-saturated Galois group with integer values
scientific article; zbMATH DE number 98391
scientific article