Jason Starr

Abstract:   This is a report of ongoing research with Johan de Jong generalizing Lang's theorem that a hypersurface of degree d in Pⁿ defined over the function field of a surface has a rational point if d² <= n. This inequality has the consequence (among many others) that the varieties parametrizing rational curves on the hypersurface are themselves rationally connected. Conjecturally, this rational connectedness implies existence of a rational point. I will discuss the strategy for proving the conjecture, why this strategy is not yet a theorem, and one important case where the conjecture is a theorem. This special case leads to a new proof and generalization of de Jong's "period-index theorem".

Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street.