Some unlikely intersections beyond André–Oort

By P. Habegger, Jonathan Pila. Compositio Mathematica, 2011

73 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fc9a7fd81a9176ae6e158abdd7e0d448025a8e75

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jacob Tsimerman
2. Martin Widmer
3. Fabrizio Barroero
4. Jonathan Pila
5. P. Habegger

In Computational Theory and Mathematics

1. Martin Widmer
2. Fabrizio Barroero
3. Jacob Tsimerman
4. P. Habegger
5. Jonathan Pila
6. Ziyang Gao
7. Umberto Zannier
8. D. Masser

In Geometry and Topology

1. Jacob Tsimerman
2. Jonathan Pila
3. Fabrizio Barroero
4. P. Habegger
5. Martin Widmer
6. Ziyang Gao
7. Bruno Klingler
8. E. Ullmo

Citations in the corpus

• Ax-Lindemann for $\mathcal{A}_g$ (2014, unknown): “It provides a geometric characterization of the exceptional set in the Counting Theorem and in this role is analogous to functional transcendence statements in the context of other Zilber-Pink type problems (e.g., [16], [23]).”
• Ax–Schanuel for the $j$-function (2014, methodology): “A special case of Theorem 1.1 (“Modular Ax-Logarithms”) is used by Habegger-Pila [11] in affirming a very special case of the Zilber-Pink conjecture for Y (1)n.”
• Towards the Andr\'e-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points (2013, unknown): “6] (Galois generic points in Ag), Habegger-Pila [31] (curves in A1 ) and Orr [43] (curves in Ag).”
• Counting Lattice Points and O-Minimal Structures (2012, methodology): “These results in turn have been applied to problems in Diophantine geometry (see [24], [22], [19], [20] and [16]).”
• Applications of the hyperbolic Ax–Schanuel conjecture (2017, unknown): “ll of the gj have coprime integer entries. As in the statement of Conjecture 12.7, we assume that X intersects F, and we let x ∈F∩X. Therefore, x = (gjτx)nj=1, where τx ∈FH. By [29], Theorem 1.2 (cf. [19], Lemma 5.2), H1(gj) ≤c1 det(gj)2, for all j ∈{1,...,n}, where c1 is a positive constant not dep”
• O-minimality and certain atypical intersections (2014, background): “For unlikely intersections of curves with special subvarieties of Y (1) partial results are obtained in [21].”