Idéaux ambiges dans les corps de fonctions

Capitulation, ambiguous classes and the cohomology of the units

“…where the map involved is induced by the natural map K * → I K,S , x → (x). Then, by (7), the above exact sequence induces an exact sequence…”

“…Assume further that K is its own S-genus field. Then the main theorem of [7], combined with ( 5), shows that (C K,S ) G trans = 0. Consequently, Theorem 2.4 yields an exact sequence…”

“…Further, let K be a finite abelian extension of F where ∞ is tamely ramified and the decomposition and inertia groups of ∞ agree. These extensions were called "of type (*)" in [7]. Assume further that K is its own S-genus field.…”