Let $G$ be a reductive $p$-adic group‎. ‎We consider the general question‎ ‎of whether the reducibility of an induced representation can be detected in a‎ ‎``co-rank one‎" ‎situation‎. ‎For smooth complex representations induced from supercuspidal‎ ‎representations‎, ‎we show that a sufficient condition is the existence of a subquotient‎ ‎that does not appear as a subrepresentation‎. ‎An import...

The Tamagawa number conjecture proposed by S. Bloch and K. Kato describes the “special values” of L-functions in terms of cohomological data. The main conjecture of Iwasawa theory describes a p-adic L-function in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of both conjectures (up to the prime 2) for L-functions attached to Dirichlet characters. We use the...

In this paper, we consider the Λ-adic deformations of Galois representations associated to elliptic curves. We prove that the Pontryagin dual of the Selmer group of a Λ-adic deformation over certain p-adic Lie extensions of a number field, that are not necessarily commutative, has no non-zero pseudo-null submodule. We also study the structure of various arithmetic Iwasawa modules associated to ...

In this paper, we prove a result on the $2$-adic logarithm of fundamental unit field $\mathbb{Q}(\sqrt[4]{-q}) $, where $q\equiv 3\bmod 4$ is prime. When 15\bmod 16$, confirms speculation Coates-Li and has consequences for certain Iwasawa modules arising in their work.