Galois theory, functional Lindemann-Weierstrass, and Manin maps

Daniel Bertrand (1) , Anand Pillay (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 UND - University of Notre Dame [Indiana]

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 equations. Using related techniques, we also give a generalization of the theorem of the kernel for abelian varieties over K.

Mots clés: Differential Galois theory; algebraic independence over function fields; semi-abelian schemes; Manin maps

Domaines: Mathématiques [math]

Daniel Bertrand, Anand Pillay. Galois theory, functional Lindemann-Weierstrass, and Manin maps. 2015. ⟨hal-01205702⟩