Rationality problems in algebraic geometry
July 29 to August 2, 2019
at the
American Institute of Mathematics,
San Jose, California
organized by
Alexander Perry,
Alena Pirutka,
and Stefan Schreieder
Original Announcement
This workshop 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).
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Papers arising from the workshop:
