Normalization in integral models of Shimura varieties of abelian type [PDF]
Mathematische Annalen, 2020 Let $(G,X)$ be a Shimura datum of Hodge type, and $\mathscr{S}_K(G,X)$ its integral model with hyperspecial level structure. We prove that $\mathscr{S}_K(G,X)$ admits a closed embedding, which is compatible with moduli interpretations, into the integral ...
Yujie Xu
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CATEGORICITY OF MODULAR AND SHIMURA CURVES [PDF]
Journal of the Institute of Mathematics of Jussieu, 2013 We describe a model-theoretic setting for the study of Shimura varieties, and study the interaction between model theory and arithmetic geometry in this setting.
Christopher Daw, A. Harris
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Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications [PDF]
Astérisque, 2020 Final version.
Bruinier, Jan +4 more
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Special cycles on toroidal compactifications of orthogonal Shimura varieties [PDF]
Mathematische Annalen, 2019 We determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define boundary components of special divisors and prove that the generating ...
J. Bruinier, Shaul Zemel
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ANDRÉ–OORT CONJECTURE AND NONVANISHING OF CENTRAL $L$ -VALUES OVER HILBERT CLASS FIELDS
Forum of Mathematics, Sigma, 2016 Let $F/\mathbf{Q}$ be a totally real field and $K/F$ a ...
ASHAY A. BURUNGALE, HARUZO HIDA
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Motivic cohomology of quaternionic Shimura varieties and level raising [PDF]
Annales Scientifiques de l'Ecole Normale Supérieure, 2019 We study the motivic cohomology of the special fiber of quaternionic Shimura varieties at a prime of good reduction. We exhibit classes in these motivic cohomology groups and use this to give an explicit geometric realization of level raising between ...
Rong Zhou
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KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES
Forum of Mathematics, Pi, 2015 We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry condition. They are formal analogs of Fourier–Jacobi expansions of Siegel modular forms.
JAN HENDRIK BRUINIER +1 more
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Remarks on generating series for special cycles on orthogonal Shimura varieties [PDF]
Algebra & Number Theory, 2019 In this note, we consider special algebraic cycles on the Shimura variety S associated to a quadratic space V over a totally real field F, |F:\Q|=d, of signature ((m,2)^{d_+},(m+2,0)^{d-d_+}), 1\le d_+
S. Kudla
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Newton Polygon Stratification of the Torelli Locus in Unitary Shimura Varieties
, 2020 We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo $p$ reduction of certain Shimura varieties. We develop a clutching method to show that the intersection of the open Torelli locus with some Newton ...
Wanlin Li +3 more
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The Modularity of Special Cycles on Orthogonal Shimura Varieties over Totally Real Fields under the Beilinson–Bloch Conjecture [PDF]
Canadian Mathematical Bulletin, 2020 AbstractWe study special cycles on a Shimura variety of orthogonal type over a totally real field of degree d associated with a quadratic form in $n+2$ variables whose signature is $(n,2)$ at e real places and $(n+2,0)$ at the remaining $d-e$ real places for $1\leq e <d$.
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