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Canonical Heights on Shimura Varieties and the Andr\'e-Oort Conjecture

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arxiv 2109.08788 v4 pith:HUVDSA2H submitted 2021-09-18 math.NT math.AG

Jonathan Pila , Ananth N. Shankar , Jacob Tsimerman , Hélène Esnault , Michael Groechenig This is my paper · ORCID
classification math.NTmath.AG
keywords andrconjecturee-oortcanonicalfullgeneralityheightsmain
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The main purpose of this work is to prove the Andr\'e-Oort conjecture in full generality.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Counting rational points on transcendental curves in valued fields

    math.NT 2025-06 conditional novelty 7.0 of 10

    In any 1-h-minimal valued field of mixed characteristic (0,p), every transcendental definable curve has at most O_epsilon(H^epsilon) rational points of height at most H.

  2. Compatibility of $F$-isocrystals on adjoint Shimura varieties

    math.NT 2025-04 conditional novelty 7.0 of 10

    For adjoint Shimura varieties in the superrigid regime, the canonical overconvergent F-isocrystal has Frobenius conjugacy classes with rational, ℓ-independent characteristic polynomials matching the canonical ℓ-adic l...

  3. What makes an algebraic curve special?

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    A survey of special curves and special subvarieties of moduli space, unifying Hodge-theoretic, Teichmüller, and bi-algebraic perspectives, with a few new results and conjectures.

  4. Unlikely intersections in Shimura varieties and beyond: a survey

    math.NT 2025-06 accept

    A survey of unlikely intersections in pure Shimura varieties, covering Andre-Oort, Andre-Pink-Zannier, Zilber-Pink, and the Pila-Zannier strategy.

  5. Hodge theory and o-minimality at CIRM

    math.AG 2025-02 unverdicted

    Survey lecture notes connecting o-minimality, Ax-Schanuel theorems, and the Zilber-Pink conjecture for Hodge loci, with no new results.

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