Noncommutative surfaces and Artin's conjecture
September 16 to September 20, 2019
American Institute of Mathematics,
San Jose, California
and Matthew Satriano
This workshop is devoted to the working on the birational classification of noncommutative surfaces and related problems. The goal is that these related results would deal with important cases in Artin's conjectured classification and make progress towards an ultimate classification.
The main topics are
- Reduction to characteristic p: Smoktunowicz has shown under general conditions that division algebras of transcendence degree 2 over finite fields are finite over their centers. Can we obtain consequences of this result in characteristic zero by using reduction to characteristic p?
- Cohen Structure Theorem: If we assume a division algebra of transcendence degree two has a valuation, can we use noncommutative analogues of Cohen's structure theorem to classify division rings with a non-trivial valuation?
- Can we show that a division algebra of transcendence degree two has a non-trivial rank one discrete valuation?
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.