Meeting Details

Title: Zero Cycles on Principal Homogeneous Spaces Algebra and Number Theory Seminar Jodi Black, Bucknell University Jean Pierre Serre has asked the following: "Let $k$ be a field, let $G$ be a connected linear algebraic group over $k$ and let $X$ be a principal homogeneous space under $G$ and over $k$. If $X$ admits a zero cycle of degree one, does $X$ have a $k$-rational point?" We use Galois Cohomology to study this question and produce a positive answer in special cases. We also consider possible extensions of this result to zero cycles of more general degree.