相关论文: On equivariant characteristic ideals of real class…

Let $G$ be a connected reductive group defined and split over a non-archimedean local field $F$. We give a new geometric proof of a special case of a recent theorem of Solleveld. Namely, we show that the class of standard Iwahori-spherical…

We investigate the group of universal norms attached to the cyclotomic Z {\ell}-tower of a totally real number field in connection with Grenberg's conjecture on Iwasawa invariants of such a field.

We consider the unramified Iwasawa module $X (F_\infty)$ of a certain $\mathbb{Z}_p$-extension $F_\infty/F_0$ generated by division points of an elliptic curve with complex multiplication. This $\mathbb{Z}_p$-extension has properties…

The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…

One of the most significant discrete invariants of a quadratic form $\phi$ over a field $k$ is its (full) splitting pattern, a finite sequence of integers which describes the possible isotropy behaviour of $\phi$ under scalar extension to…

Let $\mathbb{V}$ denote an $n$-tuple of shifts of finite multiplicity, and denote by $\mathrm{Ann}(\mathbb{V})$ the ideal consisting of polynomials $p$ in $n$ complex variables such that $p(\mathbb{V})=0$. If $\mathbb{W}$ on $\mathfrak{K}$…

We study an analogue of the Herbrand-Ribet theorem, and its refinement by Mazur and Wiles, in graph theory. For an odd prime number $p$, we let $\mathbb{F}_{p}$ and $\mathbb{Z}_{p}$ denote the finite field with $p$ elements and the ring of…

Let $K$ be a complete discrete valuation field of characteristic zero with residue field $k_K$ of characteristic $p>0$. Let $L/K$ be a finite Galois extension with Galois group $G=\Gal(L/K)$ and suppose that the induced extension of residue…

Both the Klein-Williams invariant $\ell_G(f)$ from \cite{KW2} and the generalized equivariant Lefschetz invariant $\lambda_G(f)$ from \cite{weber07} serve as complete obstructions to the fixed point problem in the equivariant setting. The…

Let $F$ be a totally real field and $K$ a finite abelian CM extension of $F$. Using class field theory, we show that our previous result giving a strong form of the Brumer-Stark conjecture implies the minus part of the equivariant Tamagawa…

This article, complement to the article [Que], deals with some generalizations of Futw\"angler's theorems for the second case of Fermat's Last Theorem (FLT2). Let $p$ be an odd prime, $\zeta$ a $p$th primitive root of unity, $K:=\Q(\zeta)$…

We study Greenberg's conjecture for cyclotomic $\mathbb{Z}_2$-extensions of real quadratic fields. Let $K=\mathbb{Q}(\sqrt{pq})$, where $$ p\equiv 1 \mod 8,\qquad q\equiv 9 \mod {16},\qquad \left(\frac{p}{q}\right)=-1. $$ Under the…

We prove a strengthening of the "reciprocity conjecture" of Khare and Wintenberger. The input to the original conjecture is an odd prime p, a CM number field F containing the pth roots of unity, and a pair of primes of the maximal totally…

The central result of this paper is a refinement of Hida's duality theorem between ordinary Lambda-adic modular forms and the universal ordinary Hecke algebra. Specifically, we give a necessary condition for this duality to be integral with…

Let $L/K$ be a Galois extension of number fields and let $G=\mathrm{Gal}(L/K)$. We show that under certain hypotheses on $G$, for a fixed prime number $p$, Leopoldt's conjecture at $p$ for certain proper intermediate fields of $L/K$ implies…

Let $\pi$ be a cuspidal, cohomological automorphic representation of an inner form $G$ of $\mathrm{PGL}_2$ over a number field $F$ of arbitrary signature. Further, let $\mathfrak{p}$ be a prime of $F$ such that $G$ is split at…

Let F be a global function field and let F^ab be its maximal abelian extension. Following an approach of D.Hayes, we shall construct a continuous homomorphism \rho: Gal(F^ab/F) \to C_F, where C_F is the idele class group of F. Using class…

Let $A$ be a finite commutative nilpotent $\mathbb{F}_p$-algebra structure on $G$, an elementary abelian group of order $p^n$. If $K/k$ is a Galois extension of fields with Galois group $G$ and $A^p = 0$, then corresponding to $A$ is an…

We consider $\mathbb{Z}_p^{\mathbb{N}}$-extensions $\mathcal{F}$ of a global function field $F$ and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as…

Let $F/E$ be a Galois extension of totally real number fields, with Galois group $\mathrm{Gal}(F/E)$. Let $\mathfrak{N}$ be an integral ideal which is $\mathrm{Gal}(F/E)$-invariant, and $k \ge 2$ an integer. In this note, we study the…