Related papers: Intersection formulas on moduli spaces of unitary …

Let $F$ be the field of rational functions on a smooth projective curve over a finite field, and let $\pi$ be an unramified cuspidal automorphic representation for $\mathrm{PGL}_2$ over $F$. We prove a variant of the formula of Yun and…

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…

This paper establishes an arithmetic intersection formula for central L-derivatives in higher weights.We prove that for a general cusp form (extending the previous result for newforms), the derivative is represented by the global height…

In this paper I'm going to study the intersection of two Heegner-Drinfeld cycles coming from two different nonsplit tori on the Yun-Zhang moduli stack of $PGL_2$ Drinfeld stukas with Iwahori level structure. We will see that the…

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…

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…

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…

Kudla has proposed a general program to relate arithmetic intersection multiplicities of special cycles on Shimura varieties to Fourier coefficients of Eisenstein series. The lowest dimensional case, in which one intersects two codimension…

We prove the higher Siegel--Weil formula for \emph{corank one} terms, relating (1) the $r^{\rm th}$ central derivatives of corank one Fourier coefficients of Siegel--Eisenstein series, and (2) the degrees of special cycles of virtual…

We extend the work of S. Zhang and Yuan-Zhang-Zhang to obtain a Gross-Zagier formula for modular forms of even weight in terms of an arithmetic intersection pairing of CM-cycles on Kuga-Sato varieties over Shimura curves. Combined with a…

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 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…

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…

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 compute the intersection multiplicities of special cycles in Lubin-Tate spaces, and formulate a new arithmetic fundamental lemma relating these intersections to derivatives of orbital integrals.

We use Picard-Lefschetz theory to prove a new formula for intersection numbers of twisted cocycles associated to a given arrangement of hyperplanes. In a special case when this arrangement produces the moduli space of punctured Riemann…

We define the Heegner--Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with $r$-modifications for an even integer $r$. We prove an identity between (1) The $r$-th central derivative of the quadratic base change…

In this paper, we obtain an explicit arithmetic intersection formula on a Hilbert modular surface between the diagonal embedding of the modular curve and a CM cycle associated to a non-biquadratic CM quartic field. This confirms a special…

In this paper, we will explain a conceptual reformulation and inductive formula of the Siegel series. Using this, we will explain that both sides of the local intersection multiplicities of [GK93] and the Siegel series have the same…

This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed the Shimura curve over Q associated to a…