Related papers: Green forms and the arithmetic Siegel-Weil formula

The goal of this paper is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific…

We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature (n-1, 1). We define arithmetic cycles on these models and study their intersection behaviour. In…

This is the third in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank $1$ for Kudla--Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even…

Let $M$ be the Shimura variety associated to the group of spinor similitudes of a quadratic space over $\mathbb{Q}$ of signature $(n,2)$. We prove a conjecture of Bruinier and Yang, relating the arithmetic intersection multiplicities of…

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. We generalize the Kudla-Millson relation between intersection numbers of cycles and Fourier coefficients of Siegel…

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…

We formulate and prove a local arithmetic Siegel--Weil formula for GSpin Rapoport--Zink spaces, which is a precise identity between the arithmetic intersection numbers of special cycles on GSpin Rapoport--Zink spaces and the derivatives of…

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 construct explicit generating series of arithmetic extensions of Kudla's special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the…

We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry condition. They are formal analogues of Fourier-Jacobi expansions of Siegel modular forms. From our result and a theorem of Wei Zhang, we deduce Kudla's…

This is the fourth in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank $1$ for Kudla--Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even…

This is the first in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank $1$ for Kudla--Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even…

On an orthogonal Shimura variety, one has a collection of special cycles in the Gillet-Soule arithmetic Chow group. We describe how these cycles behave under pullback to an embedded orthogonal Shimura variety of lower dimension. The bulk of…

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 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 describe connections between the Fourier coefficients of derivatives of Eisenstein series and invariants from the arithmetic geometry of the Shimura varieties $M$ associated to rational quadratic forms $(V,Q)$ of signature $(n,2)$. In…

We study the Faltings height pairing of arithmetic Heegner divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedian contribution to the height pairing and derive a conjecture relating the total…

For a new class of Shimura varieties of orthogonal type over a totally real number field, we construct special cycles and show the the modularity of Kudla's generating series in the cohomology group.

We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the r-th central derivative of non-singular Fourier coefficients of a normalized Siegel--Eisenstein series, and (2) the degree of special…

In this paper, we propose a modified Kudla-Rapoport conjecture for the Kr\"amer model of unitary Rapoport-Zink space at a ramified prime, which is a precise identity relating intersection numbers of special cycles to derivatives of…