We formulate a weak Gorenstein property for the Eisenstein component of the p-adic Hecke algebra associated to modular forms. We show that this weak Gorenstein property holds if and only if a weak form of Sharifi’s conjecture and a weak form of Greenberg’s conjecture hold.

We discuss three di erent formulations of the equivariant Iwasawa main conjecture attached to an extension K/k of totally real elds with Galois group G, where k is a number eld and G is a p-adic Lie group of dimension 1 for an odd prime p. All these formulations are equivalent and hold if Iwasawa's μ-invariant vanishes. Under mild hypotheses, we use this to prove non-abelian generalizations of ...

Let $$E/{\mathbb {Q}}$$ be an elliptic curve and p odd prime where E has good reduction, assume that admits a rational p-isogeny. In this paper we study the anticyclotomic Iwasawa theory of over imaginary quadratic field in which splits, relate to characters by variation method Greenberg–Vatsal. As result our obtain proofs (under relatively mild hypotheses) Perrin-Riou’s Heegner point main conj...

For a CM abelian extension F/K of an arbitrary totally real number field K, we construct the Stickelberger splitting maps (in the sense of [1]) for both the étale and the Quillen K–theory of F and we use these maps to construct Euler systems in the even Quillen K–theory of F . The Stickelberger splitting maps give an immediate proof of the annihilation of the groups of divisible elements divK2n...

Let A be the inverse limit of the p-part of the ideal class groups in a Zpextension K∞/K. Greenberg conjectures that if r is maximal, then A is pseudo-null as a module over the Iwasawa algebra Λ (that is, has codimension at least 2). We prove this conjecture in the case that K is the field of p-th roots of unity, p has index of irregularity 1, satisfies Vandiver’s conjecture, and satisfies a mi...

In this article, we study the Iwasawa theory for Hilbert modular forms over anticyclotomic extension of a CM field. We prove an one-sided divisibility result toward main conjecture in setting. The proof relies on first and second reciprocity laws relating theta elements to Heegner point Euler systems Shimura curves. As by-product also towards rank 0 case certain Bloch–Kato parity conjecture.

The main purpose of the present paper is to lay foundations generalizing AdS/CFT (holography) idea beyond conformal setting. tool find suitable realizations bulk and boundary via group theory. We use all ten families classical real semisimple Lie groups $G$ algebras $\cal G$. For this are used several algebra decompositions: global Iwasawa decomposition local Bruhat Sekiguchi-like decomposititi...