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Borcherds lift shimura variety

Web† The associated Shimura varieties † Special cycles † The special cases of signature (1,2), (2,2) 2. Theta liftings of holomorphic and weakly holomorphic modular forms † Siegel … WebTheta lifts and currents on Shimura varieties Lecture 9 Speaker: Luis Garcia Notes by: Charlotte Chan March 25, 2016 This is a write-up of a very nice talk given by Luis …

Chern classes of Heegner divisors - Massachusetts …

WebApr 11, 2024 · Charles Borchers Elementary School, in conjunction with parents and the community, is committed to the development of the whole child in a nurturing … WebNov 29, 2015 · Using the regularization of Borcherds' lift we extend the Shimura lift to take weakly holomorphic modular forms of half-integral weight to meromorphic modular forms of even integral weight having poles at CM points. Comments: 24 pages, exposition slightly modified after Equation (2), and a small typo corrected in the proof of the last … highgrove house hotel troon ayrshire https://acebodyworx2020.com

MODULARITY OF GENERATING SERIES OF DIVISORS ON …

WebDec 4, 2024 · Borcherds’ work systematically uses vector-valued modular forms, and employs the regularization technique in [ 11] to lift weakly holomorphic modular forms. … WebΨ(z,f) has a beautiful product representation called Borcherds product for its Fourier expansion near a cusp of the orthogonal Shimura variety. One of the most famous Borcherds lifts is the difference j(τ1) − j(τ2) of the well known Klein’s modular j-invariant as a modular function for SL2(Z)×SL2(Z), which is a Borcherds lift of type ... WebOct 9, 2012 · We also derive a formula for the values taken by the Borcherds products at cusps of the symmetric domain of the unitary group. Further, as an application of the lifting, we obtain a modularity result for a generating series with Heegner divisors as coefficients, along the lines of Borcherds’ generalization of the Gross-Zagier-Kohnen theorem. how i met your mother price is right episode

Abstract. arXiv:1708.08783v2 [math.NT] 9 Jan 2024

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Borcherds lift shimura variety

Shimura lifts of weakly holomorphic modular forms

WebWe are available Monday-Friday, 8:00 am – 5:00 pm by phone with lunch closure from 1-2 pm. If you have a medical need during business hours, please call the office at (970) 927 … WebOct 1, 2024 · We construct an arithmetic theta lift from harmonic Maass forms of weight 2-n to the first arithmetic Chow group of a toroidal compactification of the integral model of the unitary Shimura variety ...

Borcherds lift shimura variety

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Webthe 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 cycles on Shimura varieties associated to quadratic spaces over an arbitrary totally real base field. As a special case, we obtain an explicit formula for the norms of the CM values ... WebIn his Inventiones papers in 1995 and 1998, Borcherds constructed holomorphic automorphic forms Ψ(f) with product expansions on bounded domains D associated to rational quadratic spaces V of signature (n2), starting from vector valued modular forms f of weight 1 − n2 for SL2(Z) which are allowed to have poles at the cusp and whose …

Webdimensional Shimura variety Y !Spec(k), which can be reinterpreted as the moduli stack of el- ... on the integral model M, following the work of Borcherds [Bor98], Bruinier ... [BY09]. Using the formalism of regularized theta lifts developed in [Bor98], Bruinier [Bru02] de ned a Green function ( f) for Z(f). This Green function determines a ... WebNov 20, 2024 · This paper shows that the coordinate maps given by N. Elkies for the Shimura curves associated to the quaternion algebras with discriminants 6 and 10 are Borcherds lifts of vector-valued modular forms. This property is then used to explicitly compute the rational norms of singular moduli on these curves.

WebFinally, in Section 3.4 the singular theta-lift is used to de ne the multiplicative lifting: Borcherds products are explained as solutions of a multiplicative Cousin problem, namely of nding a meromorphic functions with divisor supported on the singularities of the singular theta-lift. We formulate a version of Borcherds’ theorem [4, Theorem WebBorcherds’ singular theta lift (e.g. [3, 6]) and established a duality statement between these two lifts. Both of these lifts have played a signi cant role in the study of certain cycles in locally symmetric spaces and Shimura varieties of orthogonal type. In this paper, we study the injectivity of the Kudla-Millson theta lift, and revisit

Webintegral model of a Shimura variety associated to a unitary group of signature pn´1,1q, and prove their modularity. The main ingredient of the proof is the calculation of the vertical components appearing in the divisor of a Borcherds product on the integral model. Contents 1. Introduction 1 2. Unitary Shimura varieties 14 3. Toroidal ...

http://www.worthequipment.com/history.htm highgrove house hotel troonWebTheta lift of Poincare series. We want to “theta lift” whmfs, and we saw it is su˝cient to ... The existence of Borcherds products plus cohomological interpretation implies that (Z;˝) = 1 4 @@log(Y2)[0] + 1 2 X ... sub-Shimura-variety corresponding to Sh U Sh?. If Uis positive or negative de˙nite, then we say the cycle is of de˙nite type. how i met your mother posterWebf is called a \Borcherds product". Unlike other lifts in the theory of modular forms, this lift is multiplicative, in the sense that f+g= f g: The weight of f is c(0)=2, where c(0) is the … how i met your mother plot