Time: 10:00-11:00, Tuesday, December 23
Venue: E14-212
Speaker: Long Liu
Titile: Trace of semi-abelian varieties and relative Mordell-Weil theorems
Abstract: Rational points on abelian varieties constitute a central subject in arithmetic geometry. This talk begins with the elliptic curve $y^2 = x^3 - x$ over Q as a concrete example to introduce the Mordell–Weil theorem, which asserts the finite generation of the group of rational points on an abelian variety. We then move to the function field setting, introducing the trace of an abelian variety and the Lang–Néron theorem—a relative version of the Mordell–Weil theorem. Finally, we present several generalizations of the trace construction and the Lang–Néron theorem to semi-abelian varieties and Deligne 1-motives.
