Related papers: Green forms and the arithmetic Siegel-Weil formula
We establish a close connection between intersection multiplicities of special cycles on arithmetic models of the Shimura variety for GU(1,2) and Fourier coefficients of derivatives of certain incoherent Eisenstein series, confirming a…
In this paper we recall the construction and basic properties of complex Shimura varieties and show that these properties actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the…
We define variants of PEL type of the Shimura varieties that appear in the context of the Arithmetic Gan-Gross-Prasad conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral…
We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings…
We study $p$-adic integral models of certain PEL Shimura varieties with level subgroup at $p$ related to the $\Gamma_1(p)$-level subgroup in the case of modular curves. We will consider two cases: the case of Shimura varieties associated…
I use methods of Chai-Hida and ordinary $p$-Hecke correspondences to study the set of irreducible components of special fibers of special cycles of sufficiently low codimension in integral models of GSpin Shimura varieties, and apply this…
This is a largely expository article based on our previous work on arithmetic diagonal cycles on unitary Shimura varieties. We define a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian…
We study the intersections of special cycles on a unitary Shimura variety of signature (n-1,1), and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of…
In this paper, we generalize a conjecture due to Darmon and Logan in an adelic setting. We study the relation between our construction and Kudla's works on cycles on orthogonal Shimura varieties. This relation allows us to conjecture a…
In a previous paper (arxiv:1409.7353), we introduced a regularized theta lift for reductive dual pairs of the form $(Sp_4,O(V))$ with $V$ a quadratic vector space over a totally real number field $F$. The lift takes values in the space of…
We use the method of Bruinier--Raum to show that symmetric formal Fourier--Jacobi series, in the cases of norm-Euclidean imaginary quadratic fields, are Hermitian modular forms. Consequently, combining a theorem of Yifeng Liu, we deduce…
For an odd prime p, we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data (G,X) of abelian type, such that G splits over a tamely ramified extension of Q_p. The local structure of…
We prove the Kudla--Rapoport conjecture for Kr\"amer models of unitary Rapoport--Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Kr\"amer models and modified derived…
We construct (cohomological) correspondences between mod $p$ fibers of different Shimura varieties and describe the fibers of these correspondences by studying irreducible components of affine Deligne-Lusztig varieties. In particular, in…
We prove that, over an arbitrary CM field, every symmetric formal Fourier-Jacobi series converges and equals the Fourier-Jacobi expansion of a genuine Hermitian Hilbert modular form. As an application, we show that the Chow-valued Kudla…
Let M be the Shimura variety associated with the group of spinor similitudes of a rational quadratic space over of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special…
We construct regular integral canonical models for Shimura varieties attached to Spin groups at (possibly ramified) odd primes. We exhibit these models as schemes of 'relative PEL type' over integral canonical models of larger Spin Shimura…
We introduce delta-forms on tropical toric varieties generalizing the construction of Mihatsch for $R^n$. These delta-forms will be used to define the star-product with Green functions of piecewise smooth type on a tropical toric variety.…
The integral model of a $\mathrm{GU}(n-1,1)$ Shimura variety carries a universal abelian scheme over it, and the dual top exterior power of its Lie algebra carries a natural hermitian metric. We express the arithmetic volume of this…
In this paper, we investigate the algebraic nature of the value of a higher Green function on an orthogonal Shimura variety at a single CM point. This is motivated by a conjecture of Gross and Zagier in the setting of higher Green functions…