We prove the conjecture of Pollack and Weston on quantitative analysis level lowering congruence à la Ribet for modular forms higher weight. It was formulated studied in context integral Jacquet–Langlands correspondence anticyclotomic Iwasawa theory weight two square-free first time. use a completely different method based $$R={\mathbb {T}}$$ theorem established by Diamond–Flach–Guo Dimitrov an...

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...

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...

We apply an equivariant version of the p-adic Weierstrass Preparation Theorem in the context of possible non-commutative generalizations of the power series of Deligne and Ribet. We then consider CM abelian extensions of totally real fields and by combining our earlier considerations with the known validity of the Main Conjecture of Iwasawa theory we prove, modulo the conjectural vanishing of c...

We prove a fundamental conjecture of Rubin on the structure local units in anticyclotomic $\mathbb{Z}_p$-extension unramified quadratic extension $\mathbb{Q}_p$ for $p\geq 5$ prime. Rubin's underlies Iwasawa theory deformation CM elliptic curve over field at primes $p$ good supersingular reduction, notably main terms $p$-adic $L$-function. As consequence, we an inequality Birch and Swinnerton-D...

We study prime ideals in skew power series rings T := R[[y; τ, δ]], for suitably conditioned complete right noetherian rings R, automorphisms τ of R, and τ -derivations δ of R. Such rings were introduced by Venjakob, motivated by issues in noncommutative Iwasawa theory. Our main results concern “Cutting Down” and “Lying Over.” In particular, assuming that τ extends to a compatible automorphsim ...