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.

  1. Understand the allowable singularities in the degeneration technique, and apply it to new classes of varieties.
  2. Compute birational invariants, e.g. unramified cohomology, in new examples, and look for new obstructions to rationality.
  3. 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.