Thesis

### Multiplicative relations among special points of modular and Shimura curves

Abstract:

We consider a number of Diophantine problems for (mixed) Shimura varieties. Specifically, we look at the multiplicative relations satisfied by special points of modular and Shimura curves. These problems are closely related to the André--Oort and Zilber--Pink conjectures, and we will resolve some special cases of these conjectures.

Let $Y$ be a modular or Shimura curve. Let $V \subset Y \times \mathbb{G}_\mathrm{m}$ be an algebraic correspondence defined over \$\overline{\mathbb{Q}}...

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Files:
• (Dissemination version, 1.0MB)

### Authors

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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

#### Contributors

Role:
Supervisor
ORCID:
0000-0003-3958-2338
More from this funder
Programme:
Studentship
Funding agency for:
Fowler, G
Grant:
1941915
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Language:
English
Keywords:
Subjects:
Deposit date:
2021-07-13