Introduction 2 1. Preliminaries 6 1.1. Algebraic modular forms 6 1.2. Modular forms over C 9 1.3. p-adic modular forms 11 1.4. Elliptic curves with complex multiplication 12 1.5. Values of modular forms at CM points 14 2. Generalised Heegner cycles 15 2.1. Kuga-Sato varieties 15 2.2. The variety Xr and its cohomology 18 2.3. Definition of the cycles 19 2.4. Relation with Heegner cycles and L-se...

Introduction. Consider a Jacobi form φ(τ, z) = ∑ n,r c(n, r)q ζ whose Fourier coefficients c(n, r) are algebraic numbers. Let p be an odd prime. In this paper we associate to φ a Λ-adic p-ordinary form in the sense of [4]. The construction comes from the map Dν introduced in [2], Theorem 3.1. This map associates to a Jacobi form a family of modular forms parametrised by ν. We obtain the two-var...

This article is the first in a series devoted to the Euler system arising from p-adic families of Beilinson-Flach elements in the first K-group of the product of two modular curves. It relates the image of these elements under the p-adic syntomic regulator (as described by Besser (2012)) to the special values at the near-central point of Hida’s p-adic Rankin L-function attached to two Hida fami...

Introduction Let Γ ⊂ PGUd−1,1(R) 0 be a torsion-free cocompact lattice. Then Γ acts on the unit ball B ⊂ C by holomorphic automorphisms. The quotient Γ\B is a complex manifold, which has a unique structure of a complex projective variety XΓ (see [Sha, Ch. IX, §3]). Shimura had proved that when Γ is an arithmetic congruence subgroup, XΓ has a canonical structure of a projective variety over some...