Results 1 to 10 of about 543 (79)
Degree and height estimates for modular equations on PEL Shimura varieties [PDF]
Journal of the London Mathematical Society, 2022 We define modular equations in the setting of PEL Shimura varieties as equations describing Hecke correspondences, and prove upper bounds on their degrees and heights. This extends known results about elliptic modular polynomials, and implies complexity bounds for number-theoretic algorithms using these modular equations. In particular, we obtain tight
Jean Kieffer
exaly +5 more sources
Forum of Mathematics, SigmaWe 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 arithmetic Chow ...
Congling Qiu, Yujie Xu
doaj +4 more sources
Semi-stable and splitting models for unitary Shimura varieties over ramified places. I. [PDF]
Forum of Mathematics, Sigma, 2023 We consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where n is even. For these varieties, we construct smooth p-adic integral models for $s=1$ and regular p-adic integral models for $s=2$ and $s=3$
Ioannis Zachos, Zhihao Zhao
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Some cases of Kudla’s modularity conjecture for unitary Shimura varieties [PDF]
Forum of Mathematics, Sigma, 2022 Abstract 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 Kudla’s conjecture on the modularity of generating series of special cycles of arbitrary codimension for ...
Jiacheng Xia
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Modularity of special cycles on unitary Shimura varieties over CM-fields [PDF]
Acta Arithmetica, 2022 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 the remaining $d-e$ real places for $1\leq e 1$, we prove that the generating series of special cycles of ...
Yota Maeda
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Modular Shimura varieties and forgetful maps [PDF]
Transactions of the American Mathematical Society, 2003 In this note we consider several maps that occur naturally between modular Shimura varieties, Hilbert-Blumenthal varieties and the moduli spaces of polarized abelian varieties when forgetting certain endomorphism structures. We prove that, up to birational equivalences, these forgetful maps coincide with the natural projection by suitable abelian ...
V. Rotger
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Kudla’s modularity conjecture on integral models of orthogonal Shimura varieties
Compositio MathematicaAbstract 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 Shimura variety recovers a result of Bruinier and Raum, originally conjectured by Kudla.
Benjamin Howard, Keerthi Madapusi
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Foliations on Shimura varieties in positive characteristic [PDF]
Journal of Algebraic Geometry, 2022 This paper is a continuation of a paper by de Shalit and Goren from 2018. We study foliations of two types on Shimura varieties S S in characteristic p p .
E. Goren, E. Shalit
semanticscholar +1 more source
Cones of special cycles of codimension 2 on orthogonal Shimura varieties [PDF]
, 2022 Let X be an orthogonal Shimura variety associated to a unimodular lattice. We investigate the polyhedrality of the cone CX of special cycles of codimension 2 on X.
Riccardo Zuffetti
semanticscholar +1 more source
Modularity of generating series of divisors on unitary Shimura varieties [PDF]
Astérisque, 2020 We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a unitary group of signature (n-1,1), and prove their modularity. The main ingredient of the proof is the calculation of the vertical components appearing in the divisor of a ...
Bruinier, Jan +4 more
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