for this workshop
Rationality problems in algebraic geometry
American Institute of Mathematics, San Jose, California
Alexander Perry, Alena Pirutka, and Stefan Schreieder
This workshop, sponsored by AIM and the NSF, will be devoted to studying rationality problems in algebraic geometry. Recently, there has been enormous progress in this area, beginning with Voisin's groundbreaking degeneration technique, and its extension by Colliot-Thelene and Pirutka, Totaro, and others. Further development of these ideas led to the proof of irrationality of many varieties that were inaccessible by earlier methods. In these arguments, the obstructions to rationality are cohomological in nature. In a different but related direction, over the past years there has been a growing supply of evidence that the derived category can also be used to detect irrationality.
The goal of this workshop is to consolidate and build on these advances, focusing on the following topics.
- Understand the allowable singularities in the degeneration technique, and apply it to new classes of varieties.
- Compute birational invariants, e.g. unramified cohomology, in new examples, and look for new obstructions to rationality.
- Study instances of the conjectural relation between rationality and derived categories, and investigate the connection to cohomological methods (like the degeneration technique).
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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