We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer–Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa μ-invariant. In combination with the authors’ previous work on the EIMC, this leads to uncond...

In this paper we prove an anticyclotomic Iwasawa main conjecture proposed by PerrinRiou for Heegner points when the global sign is −1, using a recent work of the author on one divisibility of Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic L-functions. As a byproduct we also prove the equality for the above mentioned main conjecture under some local conditions, and an improvement of...

Let $E$ be an elliptic curve with positive rank over a number field $K$ and let $p$ odd prime number. $K_{cyc}$ the cyclotomic $\mathbb{Z}_p$-extension of $K_n$ denote its $n$-th layer. The Mordell--Weil is said to constant in tower if for all $n$, $E(K_n)$ equal $E(K)$. We apply techniques Iwasawa theory obtain explicit conditions above sense. then indicate potential applications Hilbert's ten...

Let G be a real semisimple Lie group. The regular coadjoint orbits of G (a certain dense family of top-dimensional orbits) can be partitioned into a finite set of types. We show that on each regular orbit, the Iwasawa decomposition induces a left-invariant foliation which is isotropic with respect to the Kirillov symplectic form. Moreover, the dimension of the leaves depends only on the type of...

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For primes $$q \equiv 7 \ \mathrm {mod}\ 16$$ , the present manuscript shows that elementary methods enable one to prove surprisingly strong results about Iwasawa theory of Gross family elliptic curves with complex multiplication by ring integers field $$K = {\mathbb {Q}}(\sqrt{-q})$$ which are in perfect accord predictions conjecture Birch and Swinnerton-Dyer. We also some interesting phenomen...