Related papers: On two arithmetic theta lifts
We study special cycles on integral models of Shimura varieties associated with unitary similitude groups of signature (n-1,1). We construct an arithmetic theta lift from harmonic Maass forms of weight 2-n to the arithmetic Chow group of…
We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings…
With applications in the Kudla program in mind we employ singular theta lifts for the reductive dual pair $U(p,q)\times U(1,1)$ to construct two different kinds of Green forms for codimension $q$-cycles in Shimura varieties associated to…
Around 2000 Kudla presented conjectures about deep relations between arithmetic intersection theory, Eisenstein series and their derivatives, and special values of Rankin $L-$series. The aim of this text is to work out the details of an old…
Around 2000 Kudla presented conjectures about deep relations between arithmetic intersection theory, Eisenstein series and their derivatives, and special values of Rankin L-series. The aim of this text is to work out the details of an old…
We consider families of special cycles, as introduced by Kudla, on Shimura varieties attached to anisotropic quadratic spaces over totally real fields. By augmenting these cycles with Green currents, we obtain classes in the arithmetic Chow…
We show that the generating series of the number of pairs of geodesics on a compact Shimura curve with given discriminants and intersection angle are coefficients of a non-holomorphic Siegel modular form, a theta lift of the constant…
We study the modularity of the generating series of special cycles on unitary Shimura varieties over CM-fields of degree $2d$ associated with a Hermitian form in $n+1$ variables whose signature is $(n,1)$ at $e$ real places and $(n+1,0)$ at…
We consider two families of arithmetic divisors defined on integral models of Shimura curves. The first was studied by Kudla, Rapoport and Yang, who proved that if one assembles these divisors in a formal generating series, one obtains the…
Generalizing work of Gross--Zagier and Schofer on singular moduli, we study the CM values of regularized theta lifts of harmonic Whittaker forms. We compute the archimedian part of the height pairing of arithmetic special divisors and CM…
We construct a family of special cycle classes on the regular integral model of an orthogonal Shimura variety, and show that these cycle classes appear as Fourier coefficients of a Siegel modular form. Passing to the generic fiber of the…
This paper is about the arithmetic of Kudla-Rapoport divisors on Shimura varieties of type GU(n-1,1). In the first part of the paper we construct a toroidal compactification of N. Kramer's integral model of the Shimura variety. This extends…
We generalize the definition of CM cycles beyond the small and big CM ones studied by various authors and give a uniform formula for the CM values of Green functions associated to these special cycles in general using the idea of…
In previous work, we defined certain virtual fundamental classes for special cycles on the moduli stack of Hermitian shtukas, and related them to the higher derivatives of non-singular Fourier coefficients of Siegel-Eisenstein series. In…
This article sketches relations among algebraic cycles for the Shimura varieties defined by arithmetic quotients of symmetric domains for O(n,2), theta functions, values and derivatives of Eisenstein series and values and derivatives of…
We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms.…
We form a generating series of regularized volumes of intersections of special cycles on a non-compact unitary Shimura variety with a fixed base change cycle. We show that it is a Hilbert modular form by identifying it with a theta…
I employ methods from derived algebraic geometry to give a uniform moduli-theoretic construction of special cycle classes on integral models many Shimura varieties of Hodge type, including unitary, quaternionic, and orthogonal Shimura…
This paper concerns two families of divisors, which we call the `orthogonal' and `unitary' special cycles, defined on integral models of Shimura curves. The orthogonal family was studied extensively by Kudla-Rapoport-Yang, who showed that…
We study special cycles on a Shimura variety of orthogonal type over a totally real field of degree $d$ associated with a quadratic form in $n+2$ variables whose signature is $(n,2)$ at $e$ real places and $(n+2,0)$ at the remaining $d-e$…