The Brauer-Manin obstruction for singular curves and applications for surfaces
Event details
| Date | 06.12.2012 |
| Hour | 11:15 › 12:30 |
| Speaker | Yonathan Harpaz |
| Location | |
| Category | Conferences - Seminars |
The Brauer-Manin obstruction is conjectured to be essentially the only obstruction for the Hasse principle and weak approximation on smooth curves. In this talk we will show that this claim is false for singular curves. We will construct examples in which the Brauer-Manin obstruction is not enough to explain the failure of the Hasse principle and the etale-Brauer obstruction is not enough to explain the failure of weak approximation. On the positive side, we show that finite descent is the only obstruction for the Hasse principle in a certain class of singular curves. Finally, we will use the examples above to construct projective smooth surfaces for which the étale-Brauer obstruction is not the only obstruction to the Hasse principle. This is partly a joint work with Alexei Skorobogatov.
Practical information
- General public
- Free
Organizer
- CIB
Contact
- Isabelle Derivaz-Rabii