If X is a smooth, geometrically integral variety over a field k with algebraic closure k such
that the natural inclusion of Galois modules k| ! k(X)| has no section, then X has no k-points. We prove
that the converse is also true if k is a finite extension of the field of p-adic numbers, and X is a homogeneous
space of a (not necessarily affine) connected algebraic group with connected stabilizers. We construct an
example which shows that the same statement over the field of rational numbers does not hold in general.
(Joint work with Borovoi and Colliot-Th´el`ene.)

Keywords:

Homogeneous spaces, Elementary obstruction, Brauer group, local and global fields

Lecture #12279

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 12279-12779-QuickTime.mov (456 MB)

Create a DVD

You can download the video and audio files here. Please note that you need both files to create a DVD. Right click on the link and "Save As..." to save to your local computer. You can find instructions on how to create a DVD on our help page at http://www.msri.org/communications/vmath/author

• 12279-12779-DVD PCM Audio.aiff (673 MB - Audio Only)
• 12279-12779-MPEG-2 120min High Quality Encode.m2v (1535 MB - Video Only)

Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture.

If you would like to purchase a copy of this video for $15+shipping, please Click Here!

See more of our Streaming Videos on our main VMath - Streaming Video page.