A Lindemann-weierstrass Theorem for Semi-abelian Varieties over Function Fields
نویسندگان
چکیده
We prove an analogue of the Lindemann-Weierstrass theorem (that the exponentials of a Q-linearly independent set of algebraic numbers are algebraically independent), replacing Qalg by C(t)alg, and Gm by an arbitrary commutative algebraic group over C(t)alg without unipotent quotients. Both the formulations of our results and the methods have a differential algebraic flavour.
منابع مشابه
Galois theory, functional Lindemann-Weierstrass, and Manin maps
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. This paper is a continuation of [7] as well as an elaboration on the methods of Galois desc...
متن کاملN ov 2 00 8 A Lindemann - Weierstrass theorem for semiabelian varieties over function fields ∗
We prove an analogue of the Lindemann-Weierstrass theorem (that the exponentials of a Q-linearly independent set of algebraic numbers are algebraically independent), replacing Qalg by C(t)alg, and Gm by a semiabelian variety over C(t) alg. Both the formulations of our results and the methods are differential algebraic in nature.
متن کاملA Generalized Mazur’s Theorem and Its Applications
We generalize a theorem of Mazur concerning the universal norms of an abelian variety over a Zp-extension of a complete local field. Then we apply it to the proof of a control theorem for abelian varieties over global function fields.
متن کاملConstructions of Non-Abelian Zeta Functions for Curves
In this paper, we initiate a geometrically oriented study of local and global non-abelian zeta functions for curves. This consists of two parts: construction and justification. For the construction, we first use moduli spaces of semi-stable bundles to introduce a new type of zeta functions for curves defined over finite fields. Then, we prove that these new zeta functions are indeed rational an...
متن کاملTHE CONJECTURE OF TATE AND VOLOCH ON p-ADIC PROXIMITY TO TORSION
Tate and Voloch have conjectured that the p-adic distance from torsion points of semi-abelian varieties over Cp to subvarieties may be uniformly bounded. We prove this conjecture for torsion points on semi-abelian varieties over Qp using methods of algebraic model theory and a result of Sen on Galois representation of Hodge-Tate type. As a generalization of their theorem on linear forms in p-ad...
متن کامل