Research interests
I work on arithmetic and Diophantine geometry, including:
- Unlikely intersections in Shimura varieties, for example the André-Oort and Zilber-Pink conjectures.
- Arithmetic of abelian varieties and isogenies.
- The Mumford-Tate conjecture, linking the geometry and arithmetic of abelian varieties.
- Arithmetic and moduli of K3 surfaces.
Papers and preprints
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Invariant Brauer group of an abelian variety
(with A. Skorobogatov, D. Valloni and Y. Zarhin)
preprint
arXiv
-
Quantitative reduction theory and unlikely intersections
(with C. Daw)
preprint
arXiv
-
Unlikely intersections with E × CM curves in A2
(with C. Daw)
To appear in Annali della Scuola Normale di Pisa - Classe di Scienze
arXiv
-
On uniformity conjectures for abelian varieties and K3 surfaces
(with A. Skorobogatov and Y. Zarhin)
To appear in American Journal of Mathematics
arXiv
-
Galois conjugates of special points and special subvarieties in Shimura varieties
Journal of the Institute of Mathematics of Jussieu,
published online 2019-10-30
arXiv,
journal
-
Unlikely intersections with Hecke translates of a special subvariety
Journal of the European Mathematical Society 23 (1), p. 1-28, 2021
arXiv,
journal
-
Finiteness theorems for K3 surfaces and abelian varieties of CM type
(with A. Skorobogatov)
Compositio Mathematica 154 (8), p. 1571-1592, 2018
arXiv,
journal
-
Height bounds and the Siegel property
Algebra & Number Theory 12 (2), p. 455-478, 2018
arXiv,
journal
-
On compatibility between isogenies and polarisations of abelian varieties
International Journal of Number Theory 13 (3), p. 673-704, 2017
arXiv,
journal
-
Heights of pre-special points of Shimura varieties
(with C. Daw)
Mathematische Annalen 365 (3), p. 1305-1357, 2016
arXiv,
journal
The proof of Lemma 2.15 in the published version of this paper is incorrect.
The correction can be found in the arXiv version of the paper.
-
Families of abelian varieties with many isogenous fibres
Journal für die reine und angewandte Mathematik 705, p. 211-231, 2015
arXiv,
journal
There is a gap in the proof of Lemma 3.3 in the published version of this paper.
The gap was found and fixed by Gabriel Dill.
The corrections can be found in the arXiv version of the paper.
-
Lower bounds for ranks of Mumford-Tate groups
Bulletin de la Société Mathématique de France 143 (2), p. 229-246, 2015
arXiv,
journal
Survey article
-
Introduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem
in O-minimality and Diophantine Geometry, edited by G. O. Jones and A. J. Wilkie, LMS Lecture Note Series 421, 2015
pdf, publisher
PhD thesis
-
The André-Pink conjecture : Hecke orbits and weakly special subvarieties
(La conjecture d'André-Pink : orbites de Hecke et sous-variétés faiblement spéciales)
PhD thesis, Université Paris Sud, 2013
pdf
Errata for my thesis