報(bào)告人簡(jiǎn)介
葛湯立，博士畢業(yè)于布朗大學(xué)，導(dǎo)師為Dan Abramovich教授，目前在普林斯頓大學(xué)從事研究工作。研究方向?yàn)樗阈g(shù)幾何，在uniform Mordell-Lang、bounded height theorem等方向取得了一系列突出的研究成果。
內(nèi)容簡(jiǎn)介
For an abelian scheme A/S over a number field, the section group A(S) specializes to the Mordell-Weil groups on fibers. A well-known theorem of Silverman in 1983 states that if S is a curve and A/S has no constant part, then the specialization is typically injective, with an exceptional set of bounded height. I will give a generalization of Silverman's elegant theorem to higher dimensional base, as a direct application of a more general phenomenon which I call just likely intersections. I will then focus on describing the main idea in the proof, namely, homomorphism approximation, black boxing technical tools including Gao's Ax--Schanuel and Yuan--Zhang's adelic line bundles.
