David Harbater
University of Pennsilvenia " Local-global principles over semi-global fields "
Local-global principles play an important role in algebra and number theory, in the context of global fields. In recent years, such principles have been studied in a higher dimensional context, over a class of fields that have come to be known as semi-global. These include function fields of p-adic curves, and more generally one-variable function fields over complete discretely valued fields. It turns out that analogs of classical results carry over to this situation, such as the Hasse-Minkowski theorem and the theorem of Albert-Brauer-Hasse-Noether. This talk will discuss these and related results by the speaker and collaborators including J. Hartmann, D. Krashen, J-L. Colliot-Thlne, R. Parimala, and V. Suresh. |