Zhang's main contributions to number theory and arithmetical algebraic geometry are his theory of positive line bundles in Arakelov theory which he used to prove (along with E. Ullmo) the Bogomolov conjecture, and also his generalization of the Gross-Zagier theorem from elliptic curves to abelian varieties of GL(2) type over totally real fields. In particular, the latter result led him to a proof of the rank one Birch-Swinnerton-Dyer conjecture for abelian varieties of GL(2) type over totally real fields. He has also developed the theory of arithmetic dynamics.
23 Dec. 2012
返信削除on en.wiki
Zhang's main contributions to number theory and arithmetical algebraic geometry are his theory of positive line bundles in Arakelov theory which he used to prove (along with E. Ullmo) the Bogomolov conjecture, and also his generalization of the Gross-Zagier theorem from elliptic curves to abelian varieties of GL(2) type over totally real fields. In particular, the latter result led him to a proof of the rank one Birch-Swinnerton-Dyer conjecture for abelian varieties of GL(2) type over totally real fields. He has also developed the theory of arithmetic dynamics.
27 Jan. 2014
返信削除この記事に登場するShou-wu Zhang教授（Princeton UNIV.）と、双子素数の論文に登場するYitang Zhang教授（New Hampshire UNIV.）は、別人です．