Chow’s Theorem for Semi-abelian Varieties and Bounds for Splitting Fields of Algebraic Tori  

作　　者：Chia Fu YU 

机构地区：[1]Institute of Mathematics, Academia Sinica & NCTS Astronomy Mathematics Building

出　　处：《Acta Mathematica Sinica,English Series》2019年第9期1453-1463,共11页数学学报（英文版）

基　　金：supported by the MoST(Grant Nos.104-2115-M-001-001-MY3 and 107-2115-M-001-001-MY2)

摘　　要：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.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.

关 键 词：ALGEBRAIC TORI SPLITTING fields semi-abelian VARIETIES inverse GALOIS problem 

分 类 号：O153.3[理学—数学]