Results 21 to 30 of about 114 (105)

On the BDP Iwasawa main conjecture for modular forms

manuscripta mathematica, 2023
Let $K$ be an imaginary quadratic field where $p$ splits, $p\geq5$ a prime number and $f$ an eigen-newform of even weight and level $N>3$ that is coprime to $p$. Under the Heegner hypothesis, Kobayashi--Ota showed that one inclusion of the Iwasawa main conjecture of $f$ involving the Bertolini--Darmon--Prasanna $p$-adic $L$-function holds after ...
Antonio Lei, Luochen Zhao
openaire   +3 more sources

The Iwasawa Main Conjecture and Gauss Sums

Journal of Number Theory, 2001
The author gives a new proof of the main conjecture of Iwasawa theory for an imaginary abelian number field \(K\) and an odd prime number \(p\) in the semisimple case (i.e. when \(p\) does not divide \([K:\mathbb Q]\)). The technique is that of Kolyvagin's Euler systems.
openaire   +2 more sources

On exotic matrix exponential sums and Bessel–Speh functions

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract In a previous work with Carmon, we defined Bessel–Speh functions. These are matrix coefficients of irreducible Speh representations of GLkc(F)$\mathrm{GL}_{kc}(\mathbb {F})$, where F$\mathbb {F}$ is a finite field. They arise from (k,c)$(k,c)$ models, which are models that generalize the Whittaker model to Speh representations attached to ...
Elad Zelingher
wiley   +1 more source

Prismatic F‐crystals and Wach modules

Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.
Abstract We show that the category of analytic/completed prismatic F-crystals$F\text{-crystals}$ on the absolute prismatic site of a small (unramified at p$p$) base ring is naturally equivalent to the category of relative Wach modules from the theory of (φ,Γ)-modules$(\varphi, \Gamma)\text{-modules}$.
Abhinandan
wiley   +1 more source

Cohomogeneity‐one solitons in Laplacian flow: Local, smoothly‐closing and steady solitons

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract We initiate a systematic study of cohomogeneity‐one solitons in Bryant's Laplacian flow of closed G2$\text{G}_2$‐structures on a 7‐manifold, motivated by the problem of understanding finite‐time singularities of that flow. Here, we focus on solitons with symmetry groups Sp(2)${\rm Sp}(2)$ and SU(3)${\rm SU}(3)$; in both cases, we prove the ...
Mark Haskins, Johannes Nordström
wiley   +1 more source

A note on Iwasawa invariants and the main conjecture

Journal of Number Theory, 1986
[Cf. also the author, Prog. Math. 26, 287-296 (1982; Zbl 0504.12009)]. Let K be a CM-field with maximal totally real subfield k, \(G(K/k)=\{1,J\}\). The author discusses the main conjecture of Iwasawa, relating certain Galois actions to p-adic L-functions [for details and notations see \textit{L.
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An unconditional main conjecture in Iwasawa theory and applications

, 2023
We improve upon the recent keystone result of Dasgupta-Kakde on the $\Bbb Z[G(H/F)]^-$-Fitting ideals of certain Selmer modules $Sel_S^T(H)^-$ associated to an abelian, CM extension $H/F$ of a totally real number field $F$ and use this to compute the $\Bbb Z_p[[G(H_\infty/F)]]^-$-Fitting ideal of the Iwasawa module analogues $Sel_S^T(H_\infty)_p^-$ of ...
Gambheera, Rusiru, Popescu, Cristian D.
openaire   +2 more sources

On descent theory and main conjectures in non-commutative Iwasawa theory [PDF]

Journal of the Institute of Mathematics of Jussieu, 2010
AbstractWe develop an explicit descent theory in the context of Whitehead groups of non-commutative Iwasawa algebras. We apply this theory to describe the precise connection between main conjectures of non-commutative Iwasawa theory (in the spirit of Coates, Fukaya, Kato, Sujatha and Venjakob) and the equivariant Tamagawa number conjecture.
Burns, David, Venjakob, Otmar
openaire   +4 more sources

Independence and strong independence complexes of finite groups

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract Let G$G$ be a finite group. In [10], two different concepts of independence (namely, independence and strong independence) are introduced for the subsets of G$G$, yielding to the definition of two simplicial complexes whose vertices are the elements of G$G$. The strong independence complex Σ∼(G)$\tilde{\Sigma }(G)$ turns out to be a subcomplex
Andrea Lucchini, Mima Stanojkovski
wiley   +1 more source