Chow's theorem for semi-abelian varieties and bounds for splitting fields of algebraic tori

Abstract

A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper we generalize Chow's theorem to semi-abelian varieties. This contributes to different proofs of a well-known result that every algebraic torus splits over a finite separable field extension. We also obtain the best bound for the degrees of splitting fields of tori.

14 pages, to appear in Acta Math. Sinica

References in corpus (3)

• The conjugate dimension of algebraic numbers
• The inverse Galois problem for PSL_2(F_p)
• Algebraic tori - thirty years after