On the Oort conjecture for Shimura varieties of unitary and orthogonal types

DOI10.1112/S0010437X15007794zbMath1410.11066arXiv1410.5739OpenAlexW3105899162WikidataQ122921320 ScholiaQ122921320MaRDI QIDQ5360228

Xin Lu, Kang Zuo, Ke Chen

Publication date: 28 September 2017

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.5739

zbMATH Keywords

Shimura varietiesOort conjectureslope inequalityTorelli locus

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items (max. 100)

Family of curves with large unitary summand in the Hodge bundle ⋮ Slope inequality for families of curves over surfaces ⋮ Punctual characterization of the unitary flat bundle of weight one PVHS and application to families of curves ⋮ The slope of fibred surfaces: Unitary rank and Clifford index ⋮ The Oort conjecture on Shimura curves in the Torelli locus of curves ⋮ Shimura curves in the Prym locus ⋮ The Oort conjecture for Shimura curves of small unitary rank ⋮ On some differential-geometric aspects of the Torelli map ⋮ Effective estimates for the degrees of maximal special subvarieties ⋮ Massey products and Fujita decompositions on fibrations of curves ⋮ On CM points away from the Torelli locus ⋮ On the rank of the flat unitary summand of the Hodge bundle ⋮ Families of curves with Higgs field of arbitrarily large kernel

Cites Work

• Special cycles on unitary Shimura varieties. II: Global theory
• Special subvarieties arising from families of cyclic covers of the projective line
• Algebraic cycles on Shimura varieties of orthogonal type
• Fibered algebraic surfaces with low slope
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• On Kähler fiber spaces over curves
• The Oort conjecture on Shimura curves in the Torelli locus of curves
• A characterization of certain Shimura curves in the moduli stack of abelian varieties
• Symplectic representations of algebraic groups satisfying a certain analyticity condition
• Compactification of arithmetic quotients of bounded symmetric domains
• On the slope of hyperelliptic fibrations with positive relative irregularity
• The Torelli locus and special subvarieties
• Shimura Varieties in the Torelli Locus via Galois Coverings
• On Shimura curves in the Schottky locus
• Symmetry, Representations, and Invariants
• Holomorphic Imbeddings of Symmetric Domains into a Siegel Space
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