相关论文: On Jannsen's conjecture for Hecke characters of im…

Let $\mathbb{K} = \mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic number field of class number $1$ and $\mathcal{O}_{\mathbb{K}}$ its ring of integers. We study a family of Hecke $L$-functions associated to angular characters on the…

In this article, we prove a conjecture of G\"unter K\"ohler on the ambiguity of the quadratic field in the definition of Hecke theta series by deriving it from a similar statement on two-dimensional Galois representations induced from…

We consider mod $p$ Hilbert modular forms for a totally real field $F$, viewed as sections of automorphic line bundles on Hilbert modular varieties in prime characteristic $p$. For a Hecke eigenform of arbitrary weight, we prove the…

Generalised Heegner cycles are associated to a pair of an elliptic Hecke eigenform and a Hecke character over an imaginary quadratic extension $K/\Q$. Let $p$ be an odd prime split in $K/\Q$ and $l\neq p$ an odd unramified prime. We prove…

Let pi be a regular algebraic cuspidal automorphic representation of GL(2) over an imaginary quadratic number field K such that the central character of pi is invariant under the non-trivial automorphism of K. We show that pi is associated…

In previous papers we formulated an analogue of the Ichino--Ikeda conjectures for Whittaker--Fourier coefficients of automorphic forms on classical group and the metaplectic group. In the latter case we reduced the conjecture to a local…

For certain algebraic Hecke characters chi of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL_2/F. By finding congruences between Eisenstein cohomology…

Cohen and Lenstra have given a heuristic which, for a fixed odd prime $p$, leads to many interesting predictions about the distribution of $p$-class groups of imaginary quadratic fields. We extend the Cohen-Lenstra heuristic to a…

We prove that any geometrically irreducible $\overline{\mathbb{Q}}_p$-local system on a smooth algebraic variety over a $p$-adic field $K$ becomes de Rham after a twist by a character of the Galois group of $K$. In particular, for any…

We show that the action of Hecke operators away from $p$ on the space of ($p$-adic) overconvergent modular forms is ($p$-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended…

Let $p$ be an odd prime. For a number field $K$, we let $K_\infty$ be the maximal unramified pro-$p$ extension of $K$; we call the group $\mathrm{Gal}(K_\infty/K)$ the $p$-class tower group of $K$. In a previous work, as a non-abelian…

The Iwasawa main conjecture fields has been an important tool to study the arithmetic of special values of $L$-functions of Hecke characters of imaginary quadratic fields. To obtain the finest possible invariants it is important to know the…

We relate non-critical special values $p$-adic $L$-functions associated to algebraic Hecke characters of an imaginary quadratic number field with class number one to $p$-adic Coleman function called the $p$-adic Eisenstein-Kronecker series,…

The main result of the paper is a reciprocity law which proves that compatible systems of semisimple, abelian mod $p$ representations (of arbitrary dimension) of absolute Galois groups of number fields, arise from Hecke characters. In the…

Let $E/F$ be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group $GL_n(E)$ which is contragredient to its own Galois conjugate, possesses the expected distinction properties…

Let $E/K$ be a finite Galois extension of totally real number fields with Galois group $G$. Let $p$ be an odd prime and let $r>1$ be an odd integer. The $p$-adic Beilinson conjecture relates the values at $s=r$ of $p$-adic Artin…

Let X be a smooth projective curve of genus >1 over a field K which is finitely generated over the rationals. The section conjecture in Grothendieck's anabelian geometry says that the sections of the canonical projection from the arithmetic…

Let $\lambda$ be a self-dual Hecke character over an imaginary quadratic field $K$ of infinity type $(1,0)$. Let $\ell$ and $p$ be primes which are coprime to $6N_{K/\mathbb{Q}}({\mathrm cond}(\lambda))$. We determine the $\ell$-adic…

We show an Iwasawa functional equation for a two dimensional $p$-adic representation of the absolute Galois group of $\mathbf{Q}_p$. This allows us to complete Nakamura's proof of Kato's local $\epsilon$-conjecture in dimension $2$.

This article investigates congruences of $\mathfrak{p}$-adic representations arising from effective $A$-motives defined over a global function field $K$. We give a criterion for two congruent $\mathfrak{p}$-adic representations coming from…