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Multi-layer causal knowledge network for product quality problem analysis using third data. [PDF]
Sci RepWang Y, Fan R, Yue X, Li F.
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Reductions of the Main Conjecture
, 2013The main goal of this article is to discuss the relevant background needed to state the noncommutative main conjecture for certain totally real p-adic Lie extensions, and to make the important reduction to the case when the Galois group of the p-adic Lie extension is of dimension one and pro-p.
R. Sujatha
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On the non-commutative Iwasawa main conjecture for voltage covers of graphs
Israel Journal of Mathematics, 2023Let $p$ be a rational prime, and let $X$ be a connected finite graph. In this article we study voltage covers $X_\infty$ of $X$ attached to a voltage assignment ${\alpha}$ which takes values in some uniform $p$-adic Lie group $G$.
Sören Kleine, Katharina Muller
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The structure of Selmer groups and the Iwasawa main conjecture for elliptic curves
American Journal of Mathematics, 2022:We reveal a new and refined application of (a \emph{weaker} statement than) the Iwasawa main conjecture for elliptic curves to the \emph{structure} of Selmer groups of elliptic curves of \emph{arbitrary} rank.
Chan-Ho Kim
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On the BDP Iwasawa main conjecture for modular forms
Manuscripta mathematica, 2022Let K be an imaginary quadratic field where p splits, p≥5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Antonio Lei, Lu Zhao
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Non-communtative Iwasawa main conjecture
International Journal of Number Theory, 2020We formulate and prove an analogue of the non-commutative Iwasawa Main Conjecture for [Formula: see text]-adic representations of the Galois group of a function field of characteristic [Formula: see text].
M. Witte
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2021
In his important papers [16], [17], Wiles proved in most cases the so-called main conjecture for the cyclotomic Zp-extension of any totally real base field F, for all odd primes p, and for all abelian characters of Gal(Q¯ /F) (we say most cases because his work only establishes the main conjecture up to µ-invariants for those abelian characters whose ...
Coates, J, Sujatha, R
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In his important papers [16], [17], Wiles proved in most cases the so-called main conjecture for the cyclotomic Zp-extension of any totally real base field F, for all odd primes p, and for all abelian characters of Gal(Q¯ /F) (we say most cases because his work only establishes the main conjecture up to µ-invariants for those abelian characters whose ...
Coates, J, Sujatha, R
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An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications
American Journal of Mathematics, 2020:Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$-adic Lie extension whose Galois group has an abelian Sylow $p$-subgroup.
Henri Johnston, A. Nickel
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Hida duality and the Iwasawa main conjecture
Mathematische Annalen, 2019The central result of this paper is a refinement of Hida’s duality theorem between ordinary $${\varLambda }$$Λ-adic modular forms and the universal ordinary Hecke algebra. In particular, we give a sufficient condition for this duality to be integral with
Matthew J. Lafferty
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