Ramification in Iwasawa Theory and Splitting Conjectures

Chandrashekhar Khare (1) , Jean-Pierre Wintenberger (2)

1 Department of Mathematics [UCLA]
2 IRMA - Institut de Recherche Mathématique Avancée

We make a reciprocity conjecture that extends Iwasawa's analogy of direct limits of class groups along the cyclotomic tower of a totally real number field F to torsion points of Jacobians of curves over finite fields. The extension is to generalized class groups and generalized Jacobians. We state some " splitting conjectures " that are equivalent to Leopoldt's conjecture.

Domaines: Théorie des nombres [math.NT]

Chandrashekhar Khare, Jean-Pierre Wintenberger. Ramification in Iwasawa Theory and Splitting Conjectures. International Mathematics Research Notices, 2014, 2014 (1), pp.194-223. ⟨10.1093/imrn/rns217⟩. ⟨hal-01304309⟩