Towards the Andr\'e-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points
By Ziyang Gao. 2013
66 citations recorded by the source corpus.
We prove in this paper the Ax-Lindemann-Weierstrass theorem for all mixed Shimura varieties and discuss the lower bounds for Galois orbits of special points of mixed Shimura varieties. In particular we reprove a result of Silverberg in a different approach. Then combining these results we prove the Andr\'e-Oort conjecture for any mixed Shimura variety whose pure part is a subvariety of A_6^n.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/91d57d5eae5c70cd9f070655499565369fa64e05
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Pietro Corvaja
- Umberto Zannier
- Jacob Tsimerman
- Benjamin Bakker
- Jonathan Pila
- Aaron Levin
- Ziyang Gao
- Bruno Klingler
In Mathematical Physics
- Pietro Corvaja
- Umberto Zannier
- Jacob Tsimerman
- Benjamin Bakker
- Aaron Levin
- Bruno Klingler
- Jonathan Pila
- Manjul Bhargava
Citations in the corpus
- The Betti map associated to a section of an abelian scheme (2018, background): “One recognizes a special case of the notoriously difficult Dieudonn´e problem: describe vector spaces of singular (symmetric) matrices, cf. [22] 11 .”
- The Ax–Schanuel conjecture for variations of Hodge structures (2017, methodology): “The Ax–Lindemann theorem was finally established in full generality for Shimura varieties in [KUY16] by Klingler, Ullmo, and Yafaev, and for mixed Shimura varieties by Gao [Gao17].”
- Applications of the hyperbolic Ax–Schanuel conjecture (2017, unknown): “Note that pre-weakly special subvarieties of X are indeed subvarieties of X (see [16], Lemma 6.”