The local and global $varepsilon$-conjectures for the rank two case (Algebraic Number Theory and Related Topics 2014)

Abstract

This is a research anouncement of the author's article "Local ε-isomorphisms for rank two p-adic representations of Gal(Qp/Qp) and a functional equation of Kato's Euler system" (preprint, arXiv:1502.04924). In §1, we first briefly recall the formulation of the local ε-conjecture, and state our theorem concerning this conjecture for the rank two case. In §2, we first briefly recall the generalized Iwasawa main conjecture and the global ε-conjecture, and state our theorem concerning the global ε-conjecture for the rank two case.