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Seminar: Algebra and Number Theory
Homogeneous spaces over function fields of dimension two
Yi Zhu, University of Utah
Contact: R. Parimala,
Venue: Mathematics and Science Center, Room W306
Let $K$ be either a global function field or a function field of an algebraic surface. Johan de Jong formulated the following principle: a ``rationally simply connected'' $K$-variety admits a rational point if and only if the elementary obstruction vanishes. In this talk, I will discuss how this principle works for projective homogeneous spaces. In particular, it leads to a classification-free result towards the quasi-split case of Serre's Conjecture II over $K$.