Related papers: Stark-Heegner cycles attached to Bianchi modular f…

Using the framework relating hypergeometric motives to modular forms, we define an explicit family of weight 2 Hecke eigenforms with complex multiplication. We use the theory of ${}_2F_1(1)$ hypergeometric series and Ramanujan's theory of…

We show that the Euler system associated to Rankin--Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular forms vary in $p$-adic Coleman families. We prove an explicit…

Given a weight two modular form f with associated p-adic Galois representation V_f, for certain quadratic imaginary fields K one can construct canonical classes in the Galois cohomology of V_f by taking the Kummer images of Heegner points…

In this article we construct a $p$-adic three dimensional Eigenvariety for the group $U(2,1)(E)$, where $E$ is a quadratic imaginary field and $p$ is inert in $E$. The Eigenvariety parametrizes Hecke eigensystems on the space of…

The primary objective of this paper is the study of different instances of the elliptic Stark conjectures of Darmon, Lauder and Rotger, in a situation where the elliptic curve attached to the modular form $f$ has split multiplicative…

Let K be an imaginary quadratic field of discriminant -D_K<0. We introduce a notion of an adelic Maass space S_{k, -k/2}^M for automorphic forms on the quasi-split unitary group U(2,2) associated with K and prove that it is stable under the…

Let $f$ and $g$ be two modular forms which are non-ordinary at $p$. The theory of Beilinson-Flach elements gives rise to four rank-one non-integral Euler systems for the Rankin-Selberg convolution $f \otimes g$, one for each choice of…

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…

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…

Let $f \in S_{2r}(\Gamma_0(N))$ be a normalized newform of weight $2r$ which is good at $p$. Let $K$ be an imaginary quadratic field of class number one in which every prime divisor of $pN$ splits. Let $\chi$ be an anticyclotomic Hecke…

Let $K$ be an imaginary quadratic field and $p$ a prime split in $K$. In this paper we construct an anticyclotomic Euler system for the adjoint representation attached to elliptic modular forms base changed to $K$. We also relate our Euler…

Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga-Sato variety over a suitable Shimura curve which gives rise…

Given an abelian, CM extension K of any totally real number field k, we consider two conjectures `of Stark type'. The `Integrality Conjecture' concerns the image of a p-adic map `\mathfrak{s}_{K/k,S}' determined by the minus-part of the…

Let $E/\mathbb{Q}$ be an elliptic curve having multiplicative reduction at a prime $p$. Let $(g,h)$ be a pair of eigenforms of weight $1$ arising as the theta series of an imaginary quadratic field $K$, and assume that the triple-product…

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

We consider a Dirichlet series $D(F,G;s)$ attached to two automorphic forms $F$ and $G$ of an orthogonal group of real signature $(2,4)$, involving their Fourier--Jacobi coefficients. When $F$ is a Hecke eigenform and $G$ a lift of a…

We study the existence of solutions to abstract equations of the form $0 = Au + F(u)$, $u\in K\subset E$, where A is an abstract differential operator acting in a Banach space $E$, $K$ is a closed convex set of constraints being invariant…

We introduce new modified Abelian lattice models, with inhomogeneous local interactions, in which a sum over topological sectors are included in the defining partition function. The dual models, on lattices with arbitrary topology, are…

Algebraic cycles on complex projective space P(V) are known to have beautiful and surprising properties. Therefore, when V carries a real or quaternionic structure, it is natural to ask for the properties of the groups of real or…

In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that…