Ramification in Iwasawa Theory and Splitting Conjectures

Khare, Chandrashekhar; Wintenberger, Jean-Pierre
January 2014
IMRN: International Mathematics Research Notices;Jan2014, Vol. 2014 Issue 1, p194
Academic Journal
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.


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