Iwasawa’s classical asymptotical formula relates the orders of the p-parts Xn of the ideal class groups along a Zp-extension F∞/F of a number field F , to Iwasawa structural invariants λ and μ attached to the inverse limit X∞ = lim ← Xn. It relies on ”good” descent properties satisfied by Xn. If F is abelian and F∞ is cyclotomic it is known that the p-parts of the orders of the global units mod...

Let V be a crystalline p-adic representation of the absolute Galois group GK of an finite unramified extension K of Qp and T a lattice of V stable by GK . We prove the following result : Let FilV be the maximal sub-representation of V with Hodge-Tate weights strictly positive and FilT = T ∩ FilV . Then, the projective limit of the H g (K(μpn), T ) is equal up to torsion to the projective limit ...

Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions. This is possible because the combined effects of rotation, phase-shift, and attenuati...

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We begin a systematic investigation of universal norms for $p$-adic representations in higher rank Iwasawa theory. After establishing the basic properties module we construct an Iwasawa-theoretic pairing that is relevant to this setting. This allows us, example, refine classical Main Conjecture cyclotomic fields, and also give applications various well-known conjectures arithmetic concerning in...

This is an introduction to Iwasawa theory and its generalizations. We discuss some main conjectures and related subjects. Mathematics Subject Classification (2000). Primary 11R23; Secondary 11G40, 14G10.

We give a self-contained proof of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [4].