[图书][B] Point-Counting and the Zilber–Pink Conjecture
J Pila - 2022 - books.google.com
Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
Ax–Schanuel for variations of mixed Hodge structures
KCT Chiu - Mathematische Annalen, 2024 - Springer
We give properties of the real-split retraction of the mixed weak Mumford–Tate domain and
prove the Ax–Schanuel property of period mappings arising from variations of mixed Hodge …
prove the Ax–Schanuel property of period mappings arising from variations of mixed Hodge …
An overview on problems of Unlikely Intersections in families of abelian varieties
L Capuano - Expositiones Mathematicae, 2023 - Elsevier
This short survey is part of a minicourse I gave during the CMI-HIMR Summer School
“Unlikely Intersections in Diophantine Geometry” on the Zilber–Pink conjecture, formulated …
“Unlikely Intersections in Diophantine Geometry” on the Zilber–Pink conjecture, formulated …
The Relative Manin-Mumford Conjecture
Z Gao, P Habegger - arXiv preprint arXiv:2303.05045, 2023 - arxiv.org
We prove the Relative Manin-Mumford Conjecture for families of abelian varieties in
characteristic 0. We follow the Pila-Zannier method to study special point problems, and we …
characteristic 0. We follow the Pila-Zannier method to study special point problems, and we …
Effective transcendental Zilber-Pink for variations of Hodge structures
J Pila, T Scanlon - arXiv preprint arXiv:2105.05845, 2021 - arxiv.org
We prove function field versions of the Zilber-Pink conjectures for varieties supporting a
variation of Hodge structures. A form of these results for Shimura varieties in the context of …
variation of Hodge structures. A form of these results for Shimura varieties in the context of …
Ax-Schanuel with derivatives for mixed period mappings
KCT Chiu - arXiv preprint arXiv:2110.03489, 2021 - arxiv.org
arXiv:2110.03489v2 [math.AG] 19 Oct 2022 Page 1 arXiv:2110.03489v2 [math.AG] 19 Oct
2022 AX-SCHANUEL WITH DERIVATIVES FOR MIXED PERIOD MAPPINGS KENNETH …
2022 AX-SCHANUEL WITH DERIVATIVES FOR MIXED PERIOD MAPPINGS KENNETH …
Hecke orbits and the Mordell-Lang conjecture in distinguished categories
F Barroero, GA Dill - arXiv preprint arXiv:2401.11193, 2024 - arxiv.org
Inspired by recent work of Aslanyan and Daw, we introduce the notion of $\Sigma $-orbits in
the general framework of distinguished categories. In the setting of connected Shimura …
the general framework of distinguished categories. In the setting of connected Shimura …
Coloured Isomorphism of Classifiable C*-algebras
J Im - 2022 - search.proquest.com
Coloured isomorphism of classifiable C -algebras by Jeffrey Im A thesis submitted in
conformity with the requirements for the de Page 1 Coloured isomorphism of classifiable C ∗ …
conformity with the requirements for the de Page 1 Coloured isomorphism of classifiable C ∗ …
Effective computations for weakly optimal subvarieties
G Binyamini, C Daw - Journal of the European Mathematical Society, 2024 - ems.press
Ren and the second author established that the weakly optimal subvarieties (eg maximal
weakly special subvarieties) of a subvariety V of a Shimura variety arise in finitely many …
weakly special subvarieties) of a subvariety V of a Shimura variety arise in finitely many …
Zilber–Pink for raising to the power i
J Pila - Model Theory, 2024 - msp.org
The purpose of this paper is to consider the (multivalued) function w= zi through the
Schanuel–Ax–Zilber lens [Ax 1971; Zilber 2002], and in particular to formulate and prove an …
Schanuel–Ax–Zilber lens [Ax 1971; Zilber 2002], and in particular to formulate and prove an …