11 citations · 36 across the 7 of their papers we have counts for
8 papers
Pink's conjecture on unlikely intersections and families of semi-abelian varieties
Daniel Bertrand, Bas Edixhoven
The Poincaré torsor of a Shimura family of abelian varieties can be viewed both as a family of semi-abelian varieties and as a mixed Shimura variety. We show that the special subva…
Unlikely intersections in semi-abelian surfaces
Daniel Bertrand, Harry Schmidt
We consider a family, depending on a parameter, of multiplicative extensions of an elliptic curve with complex multiplications. They form a 3-dimensional variety which admits a…
Galois theory, functional Lindemann-Weierstrass, and Manin maps
Daniel Bertrand, Anand Pillay
We prove several new results of Ax-Lindemann type for semiabelian varieties over the algebraic closure K of C(t), making heavy use of the Galois theory of logarithmic differential…
Relative Manin-Mumford for semi-abelian surfaces
Daniel Bertrand, David Masser, Anand Pillay +1
We show that Ribet sections are the only obstruction to the validity of the relative Manin-Mumford conjecture for one dimensional families of semi-abelian surfaces. Applications in…
Special points and Poincaré bi-extensions, with an Appendix by Bas Edixhoven
Daniel Bertrand
The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.
Galois descent in Galois theories
Daniel Bertrand
Inspired by Kummer theory on abelian varieties, we give similar looking descriptions of the Galois groups occuring in the differential Galois theories of Picard-Vessiot, Kolchin an…