Tame topology of arithmetic quotients and algebraicity of Hodge loci

DOI10.1090/jams/952zbMath1460.14027arXiv1810.04801OpenAlexW3041080890MaRDI QIDQ5131067

Jacob Tsimerman, Benjamin Bakker, Bruno Klingler

Publication date: 2 November 2020

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.04801

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Variation of Hodge structures (algebro-geometric aspects) (14D07) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Model theory of ordered structures; o-minimality (03C64)

Related Items (21)

Sets of special subvarieties of bounded degree ⋮ Equidistribution of Hodge loci II ⋮ Volumes of definable sets in o-minimal expansions and affine GAGA theorems ⋮ Degeneration locus of \(\mathbb{Q}_p\)-local systems: conjectures ⋮ Tameness, strings, and the distance conjecture ⋮ Hodge theory, between algebraicity and transcendence ⋮ Non-linear bi-algebraic curves and surfaces in moduli spaces of abelian differentials ⋮ The Ax-Schanuel conjecture for variations of mixed Hodge structures ⋮ Bi-Yang-Baxter models and Sl(2)-orbits ⋮ Taming the landscape of effective theories ⋮ Correction to: ``Height bounds and the Siegel property ⋮ Erratum to “Tame topology of arithmetic quotients and algebraicity of Hodge loci” ⋮ On the distribution of the Hodge locus ⋮ o-minimal GAGA and a conjecture of Griffiths ⋮ Lectures on the Ax–Schanuel conjecture ⋮ Strongly minimal groups in o-minimal structures ⋮ On the geometric André-Oort conjecture for variations of Hodge structures ⋮ On the closure of the Hodge locus of positive period dimension ⋮ A note on augmented period maps ⋮ Special subvarieties of non-arithmetic ball quotients and Hodge theory ⋮ Positivity of vector bundles and Hodge theory

Cites Work

• Unnamed Item
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• The hyperbolic Ax-Lindemann-Weierstraß conjecture
• Anti-holomorphic automorphisms of the exceptional symmetric domains
• \(o\)-minimality and the André-Oort conjecture for \(\mathbb{C}^{n}\)
• The zero locus of an admissible normal function
• Analyticity of the closures of some Hodge theoretic subspaces
• Algebraic geometry and analytic geometry
• Arithmetic subgroups of algebraic groups
• Raghunathan's topological conjecture and distributions of unipotent flows
• The locus of Hodge classes in an admissible variation of mixed Hodge structure
• Zero loci of admissible normal functions with torsion singularities
• Polarized mixed Hodge structures and the local monodromy of a variation of Hodge structure
• The asymptotic behavior of a variation of polarized Hodge structure
• Reflective submanifolds. IV: Classification of real forms of Hermitian symmetric spaces
• The topology of real algebraic sets with isolated singularities
• On Raghunathan's measure conjecture
• Smooth functions invariant under the action of a compact Lie group
• On the real exponential field with restricted analytic functions
• Variation of Hodge structure: The singularities of the period mapping
• Algebraic differential equations from covering maps
• Towards the André-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points
• The André-Oort conjecture for \(\mathcal A_g\)
• Degeneration of Hodge structures
• La conjecture de Weil. I
• Geometric categories and o-minimal structures
• Definability of restricted theta functions and families of abelian varieties
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
• Ax-Schanuel for Shimura varieties
• The Ax-Schanuel conjecture for variations of Hodge structures
• Hyperbolic Ax-Lindemann theorem in the cocompact case
• Ax-Lindemann for \(\mathcal{A}_g\)
• Compactifications of locally symmetric spaces
• Groupes reductifs
• Compactification of arithmetic quotients of bounded symmetric domains
• Projections of semi-analytic sets
• A note on quotients of real algebraic groups by arithmetic subgroups
• Some metric properties of arithmetic quotients o f symmetric spaces and an extension theorem
• Height bounds and the Siegel property
• Real algebraic manifolds
• 𝑆𝐿(2)-orbit theorem for degeneration of mixed Hodge structure
• Complex analytic geometry and analytic-geometric categories
• Real forms of hermitian symmetric spaces
• The topological trace formula
• On the Locus of Hodge Classes
• Bi-algebraic geometry and the André-Oort conjecture
• On manifolds with corners
• On the algebraicity of the zero locus of an admissible normal function
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

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